11th Physics Subjective (Questions, Numerical )

 

Unit 1

Measurements

 

Subjective

 

 

Q1.      Define physics. Name its various branches. What role do the Physics play in the field of science and technology?                                                                                                                                            11101001

Q2.      What are the physical quantities? Describe international system of units in detail for            base, derived and supplementary quantities.                                                                               11101002

Q3.      What do you mean by scientific notation?                                                                                                 11101003

Q4.      What are the conventions for indicating units?                                                                             11101004

Q5.      Define errors and describe its various types.                                                                                 11101005

Q6.      What do you mean by significant figures? Describe general rules for determining them and rounding of the data.                                                                                                                                    11101006

Q7.      What do you mean by Precision and accuracy?                                                                            11101007

Q8.      What are the general rules for the assessment of total uncertainty in final result in the following cases? Explain with examples.                                                                                                         11101008

Q9.      What is meant by dimension of physical quantity? Explain its two applications.

                                                                                                                                                                                                            11101009

Short Questions

 

1.1:  Name several repetitive phenomenon occurring in nature which could serve as reasonable time standards.                                                                                                        (Board 2010,14,15) 11101010

1.2:      Give the drawbacks to use the period of a pendulum as a time standard.

 (Board 2009,14)    11101011

1.3:      Why do we find it useful to have two units for the amount of substance, the kilogram and the mole?     (Board 2015) 11101012

1.4:      Three students measured the length of a needle with a scale on which minimum division is 1 mm and recorded as (i) 0.2145 m (ii) 0.21 m (iii) 0.214m, which record is correct and why?                                              11101013

1.5:      An old saying is that “A chain is only as strong as its weakest link” What analogous statement can you make regarding experimental data used in a computation?                                                 11101014

1.6:      The period of simple pendulum is measured by a stop watch. What types of errors are possible in the time period?                                                                    (Board 2015)        11101015

1.7:      Does a dimensional analysis give any information on constant of proportionality that may appear in an algebraic expression? Explain.                                  11101016

1.8:  Write the dimensions of (i) Pressure     (ii) Density?   (Board 2009,14,15)         11101017

1.9:      The wave length l of a wave depends on the speed v of the wave and its frequency ‘f’ knowing that [l] = [L], [v] = [LT^-1] and [f] = [T^-1]. Decide which of the following is correct, f = vl or f = . 11101018

 

 

 

 

 

 

 

 

 

 

 

 

Solved Examples

 

Example 1:      The length, breadth and thickness of a sheet are 3.233m, 2.105m and 1.05cm respectively. Calculate the volume of the sheet correct upto the appropriate significant digits.  11101019

Example 2:      The mass of a metal box measured by a lever balance is 2.2kg. Two silver coins of masses 10.01g and 10.02g measured by a beam balance are added to it. What is now the total mass of the box correct upto the appropriate precision?                                          11101020

Example 3:      The diameter and length of a metal cylinder measured with the help of vernier callipers of least count 0.01 cm are 1.22 cm and 5.35 cm. Calculate the volume V of the cylinder and uncertainty in it.                                                                                                                       11101021

Example 4:      Check the correctness of the relation V =  where v is the speed of transverse wave on a stretched string of tension F, length l and mass m.                        11101022

Example 5:      Derive a relation for the time period of a simple pendulum (Fig. 1.2) using dimensional analysis. The various possible factors on which the time period T may depend are:

i)                   Length of the pendulum (l)                                                                                  11101023

ii)                Mass of the bob (m)

iii)             Angle q which the thread makes with the vertical

iv)              Acceleration due to gravity (g)

Example 6:      Find the dimensions and hence, the SI units of coefficient of viscosity h in the relation of Stokes’ law for the drag force F for a spherical object of radius r moving with velocity v given as F = 6 phrv                                                                                                                                    11101024

Numerical Problems

 

1.1: A light year is the distance light travels in one year. How many metres are there in one light year:

(speed of light = 3.0 ´ 10⁸ ms^-1)        11101025

Data:

Velocity of light = c = 3.0 ´ 10⁸ ms^-1 (constant)

Time = t = 365 ´ 24 ´ 60 ´ 60 = 31536000sec.

1.2: (a)            How many seconds are there in 1 year?                                         (Board 2014,15) 11101026

(b)  How many nanoseconds in 1 year?

(c)  How many years in 1 second?  

Data:

Largest time interval = 1 year,

Smallest time interval = 1 sec

To calculate

(a)    No. of seconds in one year.

1.3:  The length and width of a rectangular plate are measured to be 15.3 cm and 12.80cm, respectively. Find the area of the plate.                            (Board 2010)         11101027

Data:

Length of the plate = 15.3 cm

Width of the plate = 12.80cm

To calculate:

         Area of plate = ?

1.4:  Add the following masses given in kg upto appropriate precision. 2.189,0.089,11.8 and 5.32.                                 (Board 2009)  11101028

Data:

         m₁ = 2.189 kg

         m₂ = 0.089 kg

         m₃ = 11.8 kg

         m₄ = 5.32 kg

1.5:  Find the value of ‘g’ and its uncertainty using T = 2p from the following measurements made during an experiment. Length of simple pendulum  = 100 cm. Time for 20 vibrations = 40.2 sec. Length was measured by a metre scale of accuracy upto 1 mm and time by stop watch of accuracy upto 0.1 sec.             11101029

Data:

         Length of simple pendulum = 100cm

                                         =  = 1.0 m

Least count for length = 1mm = 0.001m

Time for 20 vibration   = t = 40.2 s

Least count of stop watch = 0.1s

To calculate

         Value of g = ?

1.6:  What are the dimensions and units of gravitational constant G in the formula. 

F = G                            (Board 2015)         11101030

Data:

         Formula for gravitational constant

         F = G

To calculate

         Dimensions of G = ?

1.7: Show that the expression v_f = v_i + at is dimensionally correct, where v_f is the velocity at time t.                         11101031

Data:

         Equation of motion

         v_f = v_i + at

         v_i = velocity at t = 0

         v_f = velocity at t

         a = acceleration

1.8:  The speed v of sound waves through a medium may be assumed to depend on (a) the density r of the medium and (b) its modulus of elasticity E which is the ratio of stress to strain. Deduce by the method of dimensions, the formula for the speed of sound.                                                                      11101032

Data:

Velocity of sound through medium = v

Density of the medium is =  r

Modulus of elasticity of the medium = E

To Calculate

         Relation between v, r and E.

1.9:  Show that the famous “Einstein equation” E = mc² is dimensionally consistent.

Data:                                                                           11101033

Given equation is   E = mc²

To Determine:

Equation is dimensionally consistent.

1.10: Suppose, we are told that the acceleration of a particle moving in a circle of radius r with uniform speed v is proportional to some power of r, say rⁿ, and some power of v, say v^m, determine the powers of r and v?                                              11101034

Data:

Radius of circle = r                

Uniform linear speed = v

Acceleration  = a

Power of r = n

Power of v = m

To Calculate

         n = ?, m = ?

 

 

 

 

Unit 2

Vectors and Equilibrium

               

 

 

Q1.      What is the vector quantity? How is it represented?                                                        11102001

Ans.    Vectors:

Q2.      What is meant by Rectangular Co-ordinate System or Cartesian Co-ordinate System?

                                                                                                                                                                                                            11102002

Q3.      Explain the addition of vectors.                   OR                  How are vectors added?                   11102003

Q4.      What is meant by Vector Subtraction?                                                                                          11102004

Q5. What is meant by multiplication of vector by scalar?                                                                   11102005

Q6.      Define the following terms:                                                                                                                          11102006

            (i) Position Vector     (ii) Null Vector          (iii) Equal Vector      (iv) Unit Vector

Q7.      Define Rectangular Components of Vector. How are they determined? Find their      expression.                                                                                                                                                                        11102007

Q8.How will you find a vectors magnitude and direction with the help of rectangular components?

                                                                                                                                                                                                            11101008

Q9.   Describe the method of addition of vectors by Rectangular Components.                        11102009

Q10.    State the different steps and rules for addition of vectors by rectangular components.

Q11.    How many types of vector multiplication are there? Name them.                                   11102011

Q12.    What is meant by Scalar Product? Give its examples. Describe the important             characteristics of Scalar or Dot Product.                                                                                       11102012

Q13.    Define and explain vector product. Describe its important characteristics.       11102013

Q14.    Define Torque, name its unit and hence describe the factors on which torque depends.

                                                                                                                                                                                                            11102014

Q15.    Define equilibrium. What are its types?  State and explain conditions of equilibrium.

                                                                                                                                                                                                            11102015

Short Questions

 

2.1.      Define the terms (i) unit vector (ii) Position vector (iii) Components of a vector.                                  (Board 2010, 14) 11102016

2.2       The vector sum of three vectors gives a zero resultant. What can be the orientation of vectors?                                    11102017

2.3       Vector A lies in the xy plane. For what orientations will both of its rectangular components are negative and for what orientation will its components have opposite signs?                              11102018

2.4       If one of the components of a vector is not zero, can its magnitude be zero? 
Explain.                                  (Board 2009)           11102019

2.5.      Can a vector have a component greater than the vector’s magnitude?

(Board 2010,15)         11102020

2.6.   Can the magnitude of a vector have a negative value?         (Board 2014,15) 11102021

2.7.   If A + B = 0, what can you say about the components of the two vectors?                               11102022

2.8.      Under what circumstances would a vector have component that are equal in magnitude?                                                     11102023

2.9.      Is it possible to add a vector quantity to scalar quantity? Explain.                     11102024

2.10. Can you add zero to a null vector?

                                                                                    11102025

2.11.    Two vectors have unequal magnitudes. Can their sum be zero? Explain.                                                                         11102026

2.12.    Show that the sum and difference of two perpendicular vectors of equal lengths are also perpendicular and of the same length.                                                                   11102027

2.13. How would the two vectors of the same magnitude have to be oriented, if they were to be combined to give a resultant equal to a vector of the same magnitude?                                                                         11102028

2.14.    The two vectors to be combined have magnitudes 60N and 35N. Pick the correct answer from those given below and tell why is it the only one of the three that is correct.                                                                                     11102029

   (i) 100N                   (ii)        70N                 (iii)       20N

2.15.       Suppose the sides of the closed polygon represent vector arranged head to tail. What is        the sum of these vectors?

                                                                                                        11102030

2.16.    Identify the correct answer.

(i)         Two ships X and Y are travelling in different directions at equal speeds. The actual direction of motion of X is due north but to an observer on Y, the apparent direction of motion of X is north East. The actual direction of motion of Y as observed from the shore will be:  11102031

(A) East                                  (B) West

(C) North east                        (D) South-west

(ii)              A horizontal force F applied to a small object P of mass m at rest on inclined plane at an angle q to the horizontal as shown in fig. The magnitude of the resultant force acting up and along the surface of the plane.

                                                                                                             11102032

2.17.  If all the components of the vector A₁ and A₂ were reversed, how would this alter A₁ ´ A₂?            11102033

2.18. Name the three different conditions that could make A₁ ´ A₂= 0.              11102034

Condition are:

2.19.    Identify true or false statements and explain the reason.                                     11102035

(a)               A body in equilibrium implies that it is not moving nor rotating.

2.20. A picture is suspended from a wall by two strings. Show by diagram the configuration of the strings for which the tension in the strings will be minimum.     

                                                                                                            11102036

2.21.    Can a body rotate about its centre of gravity under the action of its weight?

                                                                (Board 2009,15)  11102037

 

 

 

Solved Examples

 

Example 1:      The positions of two aeroplanes at any instant are represented by two points A (2, 3, 4) and B(5, 6, 7) from an origin O in km as shown in Fig. 2.8.                                         11102038

(i)                 What are their position vectors?

(ii)              Calculate the distance between the two aeroplanes.

Example 2:      Two forces of magnitude 10 N and 20 N act on a body in directions making angles 30^o and 60^o respectively with x-axis. Find the resultant force.                                     11102039

Example 3:      Find the angle between two forces of equal magnitude when the magnitude of their resultant is also equal to the magnitude of either of these forces.                           11102040

Example 4:      A force F = 2+ 3 units, has its point of application moved from point A(1,3)  to the point B(5,7). Find the work done.                                                                                                          11102041

Example 5:      Find the projection of vector A = 2– 8+  in the direction of the vector

B = 3– 4– 12.                                                                                         (Board 2015)            11102042

Example 6:      The line of action of a force F passes through a point P of a body whose position vector in metre is  – 2+ . If F = 2– 3+ 4 (in newton), determine the torque about the point ‘A’ whose position vector (in metre) is 2+ +                                         11102043

Example 7:      A load is suspended by two cords as shown in Fig. 2.15. Determine the maximum load that can be suspended at P, if maximum breaking tension of the cord used is 50 N.                                                                                                                                                                                     11102044

Example 8:      A uniform beam of 200N is supported horizontally as shown. If the breaking tension of the rope is 400N, how far can the man of weight 400N walk from point A on the beam as shown in Fig. 2.18?                                                                                                                11102045

Example 9:      A boy weighing 300 N is standing at the edge of a uniform diving board 4.0m in length. The weight of the board is 200 N. (Fig. 2.20 a). Find the forces exerted by pedestals on the board.                                                                                                                                                                       11102046

 

Numerical

 

2.1.      Suppose in a rectangular coordinate system, a vector A has its tail at the point P(-2, -3) and its tip at Q (3,9). Determine the distance between these two points.                                                                                          11102047

Data:   P (-2, 3)

                        Q (3, 9)

            Distance between P and Q =

2.2.      A certain corner of a room is selected as the origin of a rectangular coordinate system. If an insect is crawling on an adjacent wall at a point having co-ordinates (2,1). Where the units are in metres, what is the distance of the insect from the corner of the room?               11102048

Data:

                        Point = P = (2,1)

                        Origin = O = (0,0)

                        Formula = Origin = 0 = (0,0)

2.3.      What is the unit vector in the direction of the vector A = 4 + 3?                                                                                               11102049

2.4.      Two particles are located at
r₁= 3 + 7 and r₂ = 2 + 3 respectively. Find both the magnitude of the vector and its orientation with respect to the x axis.

Data:                                                               11102050

            r₁  = 3 + 7

            r₂  = -2 + 3

            r₂  - r₁ = ?

2.5.      If a vector B is added to vector A the result is 6 + . If B is subtracted from A the result is -4 + 7. What the magnitude of the vector A?                                        11102051

Data:

            A + B = 6 +   ---------- (1)

            A  - B = 4 + 7 --------- (2)

             = ?

 

2.6:      Given that A = 2 + 3 and
B = 3 - 4 Find the magnitude and direction of                                                    11102052

(a)        C = A + B                   (b)       D = 3A - 2B

2.7.      Find the angle between the two vectors A = 5 +  and B = 2 + 4.          11102053

Data:

            A = 5 +

            B = 2 + 4.

            q = ?

Formula:

            q = Cos^-1

2.8.            Find the work done when the point of application of the force 3 + 2 moves in a straight line from the point (2,-1) to the point (6,4).                                                     11102054

Data:

            Point A = (2, -1) =

            Point B = (6, 4) =

            Force =

2.9.      Show that the three vectors  +  + , 2 - 3 +  and 4 +  - 5 are mutually perpendicular.            (Board 2014)     11102055

2.10     Given that A =  - 2 + 3 and B = 3 - 4. Find the length of the projection of A on B.                                                            11102056

2.11.    Vectors A, B and C are 4 units north, 3 units west and 8 units east, respectively. Describe carefully                                                    11102057

(a) A ´ B                     (b) A ´ C                    (c) B ´ C

Data:

            Vector  = 4 units north

            Vector  = 3 units west

            Vector  = 8 units east

2.12.        The torque or turning effect of force about a given point given by r ´ F where r is the vector from the given point to the point of application of F. Consider a force F = -3 +  + 5 N acting on the point 7 + 3 +  (m). What is the torque in Nm about the origin?                                                 11102058

2.13. The line of action of force F =  - 2 passes through the point whose position vector is ( - + ). Find                                    11102059

(a)               the moment of F above the origin.

(b)              the moment of F about the point of which the position vector is  + .

Data: (Part-a)

           

            r =

Formula:

           

2.14.    The magnitude of dot and cross products of two vectors are 6 and 6 respectively. Find the angle between the vectors?                                      (Board 2009)  11102060

2.15. A load of 10N is suspended from a clothes lines. This distorts the line so that it makes an angle of 15° with the horizontal at each end. Find the tension in the clothes line.                                                                                   11102061

Data:

            T = ?

            W = 10N

 

2.16.    A tractor of weight 15,000N crosses a single span bridge of weight 8000N and of length 21.0m. The bridge span is supported half a metre from either end. The tractors front wheels take 1/3 of the total weight of the tractor and the rear wheals are 3m behind the front wheels. Calculate the force on the bridge supports when the rear wheel at the middle of the bridge span.        11102062

2.17.    A spherical ball of weight 50N is to be lifted over the step as shown in fig. Calculate the minimum force needed just to lift it about the floor.                          11102063

2.18.    A uniform sphere of weight 10N is held by a string attached to the frictionless wall so that the string makes an angle of 30° with the wall as shown in fig. Find the tension in the string and the force exerted on the sphere by the wall.                   11102064

 

 

 

MOTION AND FORCE

 Unit 3

 

 

 

Q.1      Define and explain the following terms in brief:                                                               11103001

            (i) Rectilinear Motion           (ii) Distance    (iii) Displacement      (iv) Velocity

            (v) Average Velocity (vi) Instantaneous Velocity               (vii) Acceleration

            (viii) Instantaneous acceleration.

Q.2 Describe different cases of velocity time graph. How acceleration can be determined from velocity time graph?                                                                                                                                       11103002

Q.3  State the three laws of motion.                                                                                                                        11103003

1.   1^st Law of Motion or (Law of Inertia):

Q.4 Define linear momentum. How are the force and linear momentum related? State Newton’s second law of motion in terms of momentum.                                                                    11103004

Q.5 Define impulse and show that it is change in momentum.                                                     11103005

Q.6 State and prove the law of conservation of linear momentum.                     (Board 2008)  11103006

Q.7      Define collision. What are its types? Define them.                                                                        11103007

Q.8      Discuss the elastic collision in one dimension and prove that speed of approach = speed of separation. Also calculate velocities after collision and discuss its special cases.11103008

Q.9 Explain the following cases of law of conservation of momentum even when the system is not isolated.                                                                                                                                                                                     11103009

            (i) Force Due to Water Flow            (ii) Momentum and Explosive Forces        

            (iii) Firing of Bullet

Q.10  What do you know by rocket propulsion? Find an expression for acceleration of rocket.                                                                                                                                                                                             11103010

Q.11    What is projectile motion? Give examples. Also derive expressions for (i) Acceleration (ii) Distance Covered (iii) Velocity at any time (iv) Time of flight (v) Range of Projectile (vi) Maximum height.                                                                                    (Board 2015)     11103011

Q.12    Write a comprehensive note on Ballistic Missile.              (Board 2008)                       11103012

Short Questions

 

3.1:      What is the difference between uniform and variable velocity? From the explanation of variable velocity, define acceleration. Give S.I units of velocity and acceleration?                          (Board 2010, 14)                11103013

3.2:      An object is thrown vertically upward. Discuss the sign of acceleration due to gravity, relative to velocity, when the object is in air.                                       11103014

3.3:      Can the velocity of an object reverse direction when acceleration is constant? If so, give an example. (Board 2010, 14,15)  11103015

3.4:  Specify the correct statements: 11103016

(a)        An object can have a constant velocity even its speed is changing.

 (b)      An object can have a constant speed even its velocity is changing.

 (c)       An object can have a zero velocity even its acceleration is not zero.

 (d)      An object subjected to a constant acceleration can reverse its velocity.

3.5:      A man standing on the top of a tower throws a ball straight up with initial velocity v_i and at the same time throws a second ball straight down with the same speed. Which ball have larger speed when it strikes the ground? Ignore air friction.                                                                           11103017

3.6:      Explain the circumstances in which the velocity v and acceleration ‘a’ of a car are:

                                                                                    11103018

3.7:      Motion with constant velocity is a special case of motion with constant acceleration. Is this statement true? Discuss.                                           (Board 2009)  11103019

3.8:      Find the change in momentum for an object subjected to a given force for a given time and state law of motion in terms of momentum.                                              11103020

3.9:      Define impulse and show that how it is related to linear momentum.

                                    (Board 2009, 10, 14)          11103021

3.10: State the law of conservation of linear momentum, pointing out the importance of isolated system. Explain why under certain conditions, the law is useful even though the system is not completely isolated. (Board 2015)  11103022

3.11: Explain difference between elastic and inelastic collisions. Explain how would a bouncing ball behave in each case? Give plausible reasons for the fact that K.E is not conserved in most cases.                 11103023

3.12:    Explain what is meant by projectile motion? Derive expressions for   

a.         the time of flight

b.         the range of projectile.

Show that the range of projectile is maximum when projectile is thrown at an angle of 45^o with the horizontal.

(Board 2014) 11103024

3.13: At what point or points in its path does a projectile have its minimum speed, its maximum speed? (Board 2014)      11103025

3.14:    Each of the following questions is followed by four answers, one of which is correct answer. Identify that answer. 11103026

1.         What is meant by the ballistic trajectory?

(a)        The paths followed by an un-powered and unguided projectile.

(b)        The path followed by the powered and unguided projectile.

(c)        The path followed by un-powered but guided projectile.

(d)       The path followed by powered and guided projectile.

2.         What happens when a system of two bodies undergoes an elastic collision?

(a)        The momentum of the system changes.

(b)        The momentum of the system does not change.

(c)        The bodies come to rest after collision.

(d)       The energy conservation Law is violated.

 

 

 

Solved Examples

 

Example 1:      The velocity-time graph of a car moving on a straight road is shown in Fig 3.7. Describe the motion of the car and find the distance covered.                                                   11103027

Example 2:      A 1500 kg car has its velocity reduced from 20 ms^–1 to 15 ms^–1 in 3.0 s. How large was the average retarding force?                                                                                                                11103028

Example 3:      Two spherical balls of 2.0 kg and 3.0 kg masses are moving towards each other with velocities of 6.0 ms^–1 and 4 ms^–1 respectively. What must be the velocity of the smaller ball after collision, if the velocity of the bigger ball is 3.0 ms^–1?                        11103029

Example 4:      A 70 g ball collides with another ball of mass 140 g. The initial velocity of the first ball is 9 ms^-1 to the right while the second ball is at rest. If the collisions were perfectly elastic. What would be the velocity of the two balls after the collision?                            11103030

Example 5:      A 100 g golf ball is moving to the right with a velocity of 20 ms^–1. It makes a head on collision with a 8 kg steel ball, initially at rest. Compute velocities of the balls after collision.                                                                                                                                                                                  11103031

Example 6:      A hose pipe ejects water at a speed of 0.3 ms^–1 through a hole of area 50 cm². If the water strikes a wall normally, calculate the force on the wall, assuming the velocity of the water normal to the wall is zero after striking.                                                                                11103032

Example 7:      A ball is thrown with a speed of 30 ms^–1 in a direction 30^o above the horizon. Determine the height to which it rises, the time of flight and the horizontal range.         11103033

Example 8:      In example 3.7 calculate the maximum range and the height reached by the ball if the angles of projection are (i) 45^o (ii) 60^o.                                                                                             11103034

 

Numericals

 

3.1       A helicopter is ascending vertically at the rate of 19.6 m/s when it is at a height of 156.8 m above the ground, a stone is dropped. How long does the stone take to reach the ground?                                        11103035

3.2:      Using the following data, draw a velocity-time graph for a short journey on a straight road of a motorbike.      11103036

3.3:      A proton moving with speed of 1.0 ´ 10⁷ m/s passes through a 0.02 cm thick sheet of paper and emerges with speed of 2.0 ´ 10⁶ m/s. Assuming uniform deceleration, find retardation and time taken to pass through the paper.         11103037

3.4:  Two masses m₁ and m₂ are initially at rest with a spring compressed between them. What is the ratio of their velocities after the spring has been released?    11103038

3.5:  An amoeba of mass 1.0 ´ 10^-12 kg propels itself through water by blowing a jet of water through a tiny orifice. The amoeba ejects water with a speed of 1.0 ´ 10^-4 m/s at a rate of 1.0 ´ 10^-13 kg m sce^-1. Assume that the water is continuously replenished so that the mass of the amoeba remains the same.

(a)    If there were no force on Amoeba other than the reaction force caused by the emerging jet, what would be the acceleration of the amoeba?

(b)    If amoeba moves with constant velocity through water, what is force of surrounding water (exclusively of jet) on the amoeba?                                                 11103039

3.6:  A boy places a fire cracker of negligible mass in an empty can of 40g mass. He plugs the end with a wooden block of mass 200 g. After igniting the fire cracker, he throws the can straight up. It explodes at the top of its path. If the block shoots out with a speed of 3m/s, how fast will the can be going?  11103040

3.7:  An electron (m = 9.1 ´ 10^-31 kg) travelling at 2.0 ´ 10⁷m/s undergoes a head on collision with a hydrogen atom (m = 1.67 ´ 10^-27 kg), which is initially at rest. Assuming the collision to be perfectly elastic and motion to be along a straight line, find the velocity of hydrogen atom.

                                                                        11103041

3.8:  A truck weighing 2500 kg and moving with a velocity of 21 m/s collides with stationary car weighing 1000 kg. The truck and the car move together after the impact. Calculate their common velocity.                                                                11103042

3.9:  Two blocks of masses 2.0 kg and 0.5 kg are attached at the two ends of a compressed spring. The elastic P.E stored in the spring is 10 J. Find the velocities of the blocks if the spring delivers its energy to the blocks when released. (Board 2008, 14)

                                                                                     11103043

3.10: A foot ball is thrown upward with an angle of 30^o with respect to the horizontal. To throw a 40m pass, what must be the initial speed of the ball?                (Board 2015) 11103044

3.11: A ball is thrown horizontal from a height of 10m with velocity of 21 m/s. How far off will it hit the ground and with what velocity?                                                                  11103045

3.12: A bomber dropped a bomb at a height of 490 m when its velocity along the horizontal was 300 km/h.         

(a)    At what distance from the point vertically below the bomber at the instant the bomb was dropped, did it strike the ground?

(b)    How long it was in air?                11103046

3.13: Find the angle of projection of a projectile for which its maximum height and horizontal range are equal.  11103047

3.14: Prove that for angle of projection, which exceed or fall short of 45^o by equal amount the ranges are equal. 11103048

3.15: A submarine launched Ballistic Missile (SLBM) is fired from a distance of 3000 km. If the ear this considered were flat and the angle of launch is 45^o with horizontal, find the time taken by SLBM to hit the target and the velocity with which the missile is fired.                       11103049

 

 

 

 

 

WORK AND ENERGY

 Unit 4

 

 

 

Q.1 Explain the meaning of work. Also define its SI unit and write its dimensions.     11104001

Q.2 Explain the work done by a variable force, also describe its graphical representation. 

                                                                                                                                                                                          11104002

Q.3      Explain the work done by Gravitational field and hence show that work done in gravitation field is independent of the path.                                  (Board 2008, 10, 14)          11104003

Q.4 Define conservative field. Give its examples. Show that work done in Gravitational is conservative field is zero.                                                                                                       (Board 2014,15) 11104004

Q.5  Differentiate between conservative and non-conservative forces.                                    11104005

Q.6      Define power and show that power is scalar product of force and velocity. Also define its SI unit.                                                                                                                                                                  11104006

Q.7 Define Kilowatt hour and establish its relation with Joule.                                                           11104007

Q.8  Define energy.    (i) K.E  (ii) P.E                                                                                                       11104008

Q.9  State and explain work energy principle.                                                                                     11104009

Q.10    Define absolute P.E an expression for it. Also find its value on the earth surface.      

                                                                                                                                                                                                                                                        11104010

Q.11    What is meant by escape velocity, derive its expression and evaluate it on earth surface.                                                                                                                                                                               11104011

Q.12    Explain the phenomenon of interconversion of K.E and P.E.              (Board 2009)  11104012

Q.13    Write a comprehensive note on the Non-Conventional sources of energy.       11104013

Short Questions

 

4.1: A person holds a bag of groceries while standing still, talking to a friend. A car is stationary with its engine running. From the stand point of work, how are these two situations similar?                 11104014

4.2: Calculate the work done in kilo joules in a lifting a mass of 10 kg (at a steady velocity) through a vertical height of 10m.                                          (Board 2009, 14) 11104015

4.3: A force F acts through a distance L. The force is then increased to 3F and then acts through a further distance of 2L. Draw the work diagram to scale.(Board 2015) 11104016

4.4: In which case is more work done? When a 50 kg bag of books is lifted through 50cm or when a 50kg crate is pushed through 2m across the floor with a force of 50N.                          (Board 2010)  11104017

4.5: An object has 1J of potential energy. Explain what does it mean?             11104018

4.6: A ball of mass m is held at a height h₁ above a table. The table top is at a height h₂, above the floor. One student says that the ball has potential energy mgh₁ but another says that it is mg (h₁ + h₂) who is correct.                                                                11104019

4.7: When a rocket re-enters the atmosphere, its nose cone becomes very hot, from where does this heat energy come from?                       (Board 2010)          11104020

4.8: What sort of energy is in the following?                (Board 2009,15)   11104021

      (i) Compressed Spring

      (ii) Water Dam

      (iii) Moving Car

4.9: A girl drops a cup from a certain height, which breaks into pieces. What energy changes are involved?  (Board 2014)

11104022

4.10:    A boy uses a catapult to throw a stone which accidentally smashes a green house window. List the possible energy changes.

                                    (Board 2015)     11104023

 

 

 

Solved Examples

 

Example 1:      A force F acting on an object varies with distance x as shown in . Calculate the work done by the force as the object moves from x = 0 to x = 6 m.                                        11104024

Example 2:      A 70 kg man runs up a long flight of stairs in 4.0 s. The vertical height of the stairs is 4.5m. Calculate his power output in watts.                                                                         11104025

Example 3:      A brick of mass 2.0 kg is dropped from a rest position 5.0 m above the ground. What is its velocity at a height of 3.0 m above the ground?                                                                 11104026

 

 

Numerical Problems

 

4.1: A man pushes a lawn mower with a 40N force directed at an angle of 20^o downward from the horizontal. Find the work done by the man as he cuts a strip of grass 20m long.                                        11104027

Data:

      F = 40 N

      q = 20°

      d = 20 m

      W = F. d = ?

4.2: A rain drop m = 3.35 ´ 10^-5 kg falls vertically at a constant speed under the influence of the forces of gravity and friction. In falling through 100m, how much work is done by:                                   11104028

(a) Gravity:

(b) Friction:

Data:   m = 3.35 ´ 10^-5 kg

h = 100 m

W_g = work done due to gravity = ?

W_f = work done due to friction  = ?

4.3: Ten bricks, each 6cm thick and mass 1.5kg, lie flat on a table. How much work is required to stack them one on the top of another.                                                                    11104029

Data: m = 1.5kg

      height of each brick h = 6 cm = 0.06 m

No. of bricks = 10

      Net work done = W = ?

4.4: A car of mass 800kg travelling at 54km/h is brought to rest in 60 metres. Find the average retarding force on the car. What has happened to original K.E?

Data:                                                               11104030

m = 800 kg vi = 54 km/h      == 15 m/s vf = 0 m/s

      d = 60 m

      F = ?

4.5: A 1000 kg automobile at the top of an inclined plane 10m high and 100m long is released and rolls down the hill. What is its speed at the bottom of the incline if the average retarding force due to friction is 480N?                                   (Board 2008)  11104031

Data:   m = 1000 kg

            h = 10 m

            d = 100 m

            F = 480 N

4.6: 100m³ of water is pumped from a reservoir into a tank, 10m higher than the reservoir, in 20 minutes. If density of water is 1000kg m^-3, find                       11104032

(a)  The increase in P.E

(b)  The power delivered by pump.     

Data: volume of water = V = 100 m³

      = 1000 kgm^-3

      h =  10 m

      t = 20 min = 20 ´ 60 = 1200 sec

      P. E = ?

           Power = ?

4.7: A force (thrust) of 400N is required to overcome road friction and air resistance in propelling an automobile at 80km/h. What power (kW) must the engine develop?                                                                                    11104033

Data:

      v = 80 km/h

         = m/sec.

v  = 22.2 m/s

F = 400 N

q = 0

P = ?

4.8: How large a force is required to accelerate an electron (m = 9.1 ´ 10^-31 kg) from rest to a speed of (2 ´ 10⁷ m/s) through a distance of 5 cm.                       11104034

Data:   m = 9.1 ´ 10^-31 kg

            v_i = 0

            v_f = 2.0 ´ 10⁷ m/s

            d = 5cm = 0.05 m

            F = ?

4.9: A diver weighing 750N dives from a board 10m above the surface of the pool of water. Use the conservation of mechanical energy to find his speed at a point 5m above the water surface, neglecting air friction.                                                                    11104035

Data:  

            v_i = 0 m/sec

            h = 10m

            h₁ = 5m

            v_f = ?

4.10: A child starts from rest at the top of a slide of height 4m. (a) What is his speed at the bottom if the slide is frictionless? (b) If he reaches the bottom, with a speed of 6m/s. What percentage of his total energy at the top of the slide is lost as a result of friction?                                                                11104036

Data:   v_i = 0 m/sec

            v_f = ?

            h = 4m

            = 6 m/s

Percentage loss of total energy = ?

 

 

 

Circular Motion

 Unit 5

 

 

 

Q.1  Define circular motion. Also give example.                                                                                        11105001

Q.2 Define angular displacement. Also write its unit.                                                              11105002

Q.3 Define Radian. Establish the relation  and show that 1 radian = 57.3^o       11105003

Q.4  Define angular velocity. Establish relation v = wr.                                                                       11105004

Q.5  Define angular acceleration. How is it related with linear acceleration?              11105005

Q.6 Write the brief review of equation of uniformly accelerated body with angular acceleration.                                                                                                                                                                        11105006

Q.7      Define centripetal force. Derive the expression of centripetal force in terms of angular velocity.                                                                                                                                                                    11105007

Q.8 Define and explain moment of inertia of right body and its significance. OR    11105008

      What is moment of inertia? Find the expression for moment of inertia of a rigid body.

Q.9 Define and explain the term angular momentum.                                                             11105009

Q.10    State and explain the law of conservation of momentum and write its few applications in sports.                                                                                                                                                                                                                                                                                                                                       11105010

Q.11    Define Rotational K.E of rigid body. Derive its expression.                                         11105011

Q.12    Find the K.E of disc and hoop rolling on smooth surface of an incline plane. Using Law of conservation of energy, find their velocities at the bottom of inclined plane.                             11105012

 

Q.13    What are Artificial Satellite? Find the expression of orbital speed of satellite orbiting very close to the earth and evaluate it.                                                                                                                                                                                                                                                              11105013

Q.14    What do you mean by Global Positioning System.                                                                  11105014

Q.15    Define real and apparent weight. Establish relation between real and apparent weight of body. Discuss all it cases in an elevator.                                                                         11105015

Q.16    Explain the weightlessness in satellite.                                                                                           11105016

Q.17    Derive an expression of orbital speed of satellite. How does it depends upon orbital radius?                                                                                                                                                                    11105017

Q.18    What are Geostationary satellites? Derive an expression for the radius of Geo Stationary satellite.                                                                                                                           11105018

Q.19    What are communication satellites?                                                                                              11105019

Q.20    Describe a brief view about Newton and Einstein theory about gravitation. Why Einstein theory is considered to be most general one?                                                     11105020

Short Questions

 

5.1: Explain the difference between tangential velocity and angular velocity. If one of these is given for a wheel of known radius, how will you find the other?

             (Board 2010)   11105021

5.2: Explain what is meant by centripetal force and why it must be furnished to an object if the object is to follow a circular path?                              (Board 2009,15)                11105022

5.3: What is meant by moment of Inertia? Explain its significance.     (Board 2010,15) 11105023

5.4:What is meant by angular momentum? Explain the law of conservation of angular momentum.                               11105024

5.5: Show that angular momentum L_o = mvr.                          (Board 2014,15) 11105025

5.6: Describe what should be the minimum velocity, for a satellite, to orbit close to the Earth around it.

                                    (Board 2010) 11105026

5.7: State the direction of the following vectors in simple situations, angular momentum and angular velocity.   11105027

5.8: Explain why an object orbiting the earth is said to be freely falling. Use your explanation to point out why objects appear with weightless under certain circumstances.                                            11105028

5.9: When mud flies off the tyre of a moving bicycle, in what direction does it fly? Explain.                  (Board 2015)  11105029

5.10: A disc and a hoop start moving down from the top of an inclined plane at the same time. Which one will be moving faster on reaching the bottom?                                11105030

5.11: Why does a diver change his body positions before and after diving in the pool?                          (Board 2009)   11105031

5.12: A student holds two dumb-bells with stretched arms while sitting on a turn table. He is given a push until he is rotating at certain angular velocity. The student then pulls the dumb-bells towards his chest. What will be the effect on rate of rotation?                                                                        11105032

5.13: Explain how many minimum numbers of geo-stationary satellites are required for global coverage of T.V. transmission?                                                        11105033

 

 

Solved Examples

 

Example 1:      An electric fan rotating at 3 rev s^-1 is switched off. It comes to rest in 18.0 s. Assuming deceleration to be uniform, find its value. How many revolutions did it turn before coming to rest?                                                                                                                                                          11105034

Example 2:      A 1000 kg car is turing round a corner at 10 ms^-1 as it travels along an arc of a circle. If the radius of the circular path is 10 m, how large a force must be exerted by the pavement on the tyres to hold the car in the circular path?                                                             11105035

Example 3:      A ball tied to the end of a string, is swung in a vertical circle of radius r under the action of gravity as shown in Fig. 5.7. What will be the tension in the string when the ball is at the point A of the path and its speed is v at this point?                                                                 11105036

Example 4:      The mass of Earth is 6.00 ´ 10²⁴ kg. The distance r from Earth to the Sun is 1.50 ´ 10¹¹ m. As seen from the direction of the North Star, the Earth revolves counter-clockwise around the Sun. Determine the orbital angular momentum of the Earth about the Sun, assuming that it traverses a circular orbit about the Sun once a year (3.16 ´ 10⁷s). 11105037

Example 5:      A disc without slipping rolls down a hill of height 10.0 m. If the disc starts from rest at the top of the hill, what is its speed at the bottom?                                                    11105038

Example 6:      An Earth satellite is in circular orbit at a distance of 384,000 km from the Earth’s surface. What is its period of one revolution in days? Take mass of the Earth M = 6.0 ´ 10²⁴kg and its radius R = 6400 km.                                                                                                                  11105039

Example 7:      Radio and TV signals bounce from a synchronous satellite. This satellite circles the Earth once in 24 hours. So if the satellite circles eastward above the equator, it stays over the same spot on the Earth because the Earth is rotating at the same rate. (a) What is the orbital radius for a synchronous satellite? (b) What is its speed?                   11105040

 

Numerical Problems

 

5.1: A tiny laser beam is directed from the Earth to the Moon. If the beam is to have a diameter of 2.50 m at the Moon, how small must divergence angle be for the beam? The distance of moon from the earth is 3.8´10⁸m.                                         11105041

5.2: A gramophone record turntable accelerates from rest to an angular velocity of 45.0rev min^-1 in 1.60s. What is its average angular acceleration? 11105042

5.3: A body of moment of inertia
I=0.80kg m² about a fixed axis, rotates with a constant angular velocity of 100rad s^-1. Calculate its angular momentum L and torque to sustain this motion.               11105043

5.4:   Consider the rotating cylinder shown in Fig. Suppose that m = 5.0kg, F = 0.60N and r = 0.20m. Calculate:  

(a) The torque acting on the cylinder.

(b) The angular acceleration of the cylinder.                                                              11105044

5.5: Calculate the angular momentum of a star of mass 2.0 ´10³⁰kg and radius 7.0 ´ 10⁵km. If it makes one complete rotation about its axis once in 20 days, what is its K.E?                            (Board 2010)        11105045

5.6: A 1000kg car travelling with a speed of 144 km h^-1 rounds a curve of radius 100m. Find the necessary centripetal force.

                                                                        11105046

5.7: What is the least speed at which an aeroplane can execute a vertical loop of 1.0km radius so that there will be no tendency for the pilot to fall down at the highest point?            (Board 2015)   11105047

5.8: The moon orbits the Earth so that the same side always faces the Earth. Determine the ratio of its spin angular momentum (about its own axis) and its orbital angular momentum. (In this case, treat the Moon as a particle orbiting the Earth). Distance between the Earth and the Moon is 3.85 ´ 10⁸m. Radius of the Moon is 1.74 ´ 10⁶m.                                 11105048

5.9: The earth rotates on its axis once a day. Suppose by some process the Earth contracts so that its radius is only half as large as at present. How fast will it be rotating then? (For Sphere I = 2/5 MR²).

            `                                                           11105049

5.10: What should be the orbiting speed to launch a satellite in a circular orbit 900km above the surface of the Earth? (Take mass of the earth as 6.0 ´ 10²⁴ and its radius as 6400km).               (Board 2015)  11105050

 

 

 

 

 

 

Unit 6

 

FLUID DYNAMICS

 

Q.1 Define the terms fluid dynamics, fluid and viscosity.                                                                    11106001

Q.2 Define Drag Force. What are the factors of its dependence?                                             11106002

Q.3 State the Stoke’s law.                                                                                                                          11106003

Q.4      Define Terminal Velocity of body and show that terminal velocity is directly proportional to the square of radius of body.                                                (Board 2015)     11106004

Q.5 Differentiate between stream line flow and turbulent flow.                                               11106005

Q.6 What is an ideal fluid? State and prove equation of continuity.  (Board 2010) 11106006

Q.7 State and prove Bernoulli’s Equation in dynamic fluid, that relates pressure to fluid speed and height. .                                                                                                       (Board 2015)               11106007

Q.8 Describe the following applications of Bernoulli’s Equation.                                            11106008

      (i) Torricelli’s Theorem    (ii) Relation between speed and pressure

      (iii) Venturi Relation

Q.9      Explain the blood flow in the human body. Describe working of sphygmomanometer used for measuring upper and lower limits of blood pressure.                                           11106009

 

Short Questions

 

6.1: Explain what do you understand by the term viscosity?   (Board 2008,10,14) 11106010

6.2: What is meant by the drag force, what are the factors upon which drag force acting upon a small sphere of radius r, moving down through a liquid depend?

                                                                        11106011

6.3: Why fog droplets appear to be suspended in air? (Board 2010,14,15) 11106012

6.4: Explain the difference between laminar flow and turbulent flow?

                                                (B. 2008, 2009,15)   11106013

6.5: State Bernoulli’s relation for a liquid in motion and describe some of its application?                              (B. 2009)             11106014

6.6: A person is standing near a fast moving train. Is there any danger that he fall towards it?                       (B. 2008)             11106015

6.7: Identify the correct answer according to Bernoulli’s effect.                                      11106016

6.8: Two row boats moving parallel in the same direction are pulled towards each other. Explain.           (Board 2010)  11106017

6.9: Explain how the swing is produced in a fast moving cricket ball.

                                                (Board 2009)  11106018

6.10:    Explain the working of a carburetor of a motor car using Bernoulli’s principle.

                                                                        11106019

6.11:    For which position will the maximum blood pressure in the body has the smallest value: (a) standing up right (b) sitting (c) lying horizontally (d) standing on one’s head?                                                                  11106020

6.12:    In an orbiting space station would the blood pressure in major arteries in the leg ever be greater than the blood pressure on major arteries in the neck?                  11106021

 

Solved Examples

 

Example 1:      A tiny water droplet of radius 0.010 cm descends through air from a high building. Calculate its terminal velocity. Given that h for air = 19 ´ 10^-6 kg m^-1 s^-1 and density of water r = 1000 kgm^-3.                                                                                                                                           11106022

Example 2:      A water hose with an internal diameter of 20 mm at the outlet discharges 30 kg of water in 60s. Calculate the water speed at the outlet. Assume the density of water is 1000 kgm^-3 and its flow is steady.                                                                                                                   11106023

Example 3:      Water flows down hill through a closed vertical funnel. The flow speed at the top is 12.0 cms^-1. The flow speed at the bottom is twice the speed at the top. If the funnel is 40.0 cm long and the pressure at the top is 1.013 ´ 10⁵ Nm^-2, what is the pressure at the bottom?                                                                                                                                                                                  11106024

Numerical Problems

 

6.1: Certain globular protein particle has a density of 1246 Kgm^-3. It falls through pure water (h = 8.0 x 10^-4 N m^-2 s) with a terminal speed of 3.0 cm h^-1. Find the radius of the particle.                               11106025

Data:

      r = 1246 Kg^-3

      h = 8.0 ´ 10^-4 N m^-2 s

            v_t = 3.0 cm/h

       =

            v_t = 8.33 ´ 10^-6 m/s

      r = ?

 

6.2: Water flows through a hose, whose internal diameter is 1 cm, at a speed of 1ms^-1. What should be the diameter of the nozzle if the water is to emerge at 21ms^-1?    11106026

Data:                                                  

      D₁ = 1 cm = m = 0.01 m.

      v₁ = 1 m s^‑1

      D₂ = ?

      v₂ = 21 m s^-1

6.3: The pipe near the lower end of a large water storage tank develops a small leak and a stream of water shoots from it. The top of water in the tank is 15m above the point of leak.                                                 11106027

(a) With what speed does the water rush from the hole?

(b) If the hole has an area of 0.060 cm² how much water flows out in one second?

Data:

      h = 15 m

      A = 0.060 cm²

                = 0.060 ´ 10^-4 m²

      A = 6.0 ´ 10^-6 m²

      v =?

      Rate of flow =?

6.4: Water is flowing smoothly through a closed pipe system. At one point the speed of water is 3m s^-1 while at another point 3m higher, the speed is 4.0 m s^-1. If pressure is 80 kPa at the lower point, what is pressure at the upper end?            11106028

Data:

      v₁ = 3 m s^-1

      P₁ = 80 kPa = 80,000 Pa

      v₂ = 4 m s^-1

      h₂ - h₁ = 3m

      r  = 1000 kg m^-3

      P₂ = ?

6.5: An air plane wing is designed so that when the speed of air across the top of the wing is 450 m s^-1, the speed of air below the wing is 410 m s^-1. What is the pressure difference between the top and bottom of the wing? (density of air = 1.29 kg m^-3).

Data:                                                                           11106029

      v₁ = 410 m s^-1

      v₂ = 450 m s^-1

      r = 1.29 kgm^-3

      P₁ - P₂ = ?

6.6: The radius of the aorta is about 1.0 cm and the blood flowing through it has a speed of about 30 cms^-1. Calculate the average speed of the blood in the capillaries, using the fact that although each capillary has a diameter of about 8 ´ 10^-4 cm, these are literally millions of them so that the total cross section is about 2000 cm².                                                                       11106030

Data:

       r₁ = 1 cm = 0.01 m

v₁ = 30 cm s^-1 =  m s^-1 = 0.30 m s^-1

A₂ = 2000 cm² = 2000 ´ 10^-4 m²

A₂ = 0.2 m²

v₂ = ?

6.7: How large must a heating duct be if air moving 3.0 ms^-1 along it can replenish the air in a room of 300 m³ volumes every 15min? Assume the air’s density remains constant.                                                              11106031

Data:

      t = 15min = 15 ´ 60 s = 900 s

      Volume of air =V = 300 m³

      v = 3 m s^-1

      r = ?

6.8: An airplane design calls for a “lift” due to the net force of the moving air on the wing of about 1000N m^-2 of wing area. Assume that air flows past the wing of an air craft with streamline flow. If the speed of flow past the lower wing surface is 160ms^-1, what is the required speed over the upper surface to give a “lift” of 1000Nm^-2? The density of air is 1.29 kgm^-3 and assume maximum thickness of wing to be one metre.                                                    11106032

Data:

      P₁ - P₂ = 1000 N m^-2

      V₁ = 160 m s^-1

      V₂ = ?

      r = 1.29 kg m^-3

      h₂ – h₁ = 1 m

6.9: What gauge pressure is required in the city mains for a stream from a fire hose connected to the mains to reach a vertical height of 15 m?                          11106033

Data:

h = 15 m

g = 9.8 m s^-2

r = 1000 kg m^-3

Gauge pressure = P₁ - P₂ = ?

 

 

Unit 7

 

OSCILLATIONS

 

 

 

 

Q.1 Define Vibratory Motion. Give examples and its types.                                                     11107001

Q.2 Define Restoring force.                                                                                                                                   11107002

Q.3 Define and explain Simple Harmonic Motion.                                                                               11107003

Q.4 Define the following terms:                                                                                                                             11107004

      (i) Displacement                (ii) Amplitude              (iii) Vibration

      (iv) Time period                 (v) Frequency              (vi) Angular frequency

Q.5 Co-relating  simple harmonic motion and uniform circular motion. Derive expression for the following:                                                                                                                                                       11107005

      (i) Displacement    (ii) Instantaneous Velocity      (iii) Acceleration

Q.6   Discuss the characteristics of the mass attached to the horizontal spring and moving on a smooth surface.                                                                                                                                                    11107006

Q.7   Describe simple pendulum. Show that it executes S.H.M when its amplitude kept in small. Find expression for the time period.                                                                                                     11107007

Q.8 Explain the energy conservation law in S.H.M.                                                                                                 11107008

Q.9 Define free and forced oscillation.                                                                                                       11107009

Q.10 Define and explain resonance. Give examples.                                                                            11107010

Q.11 What do you mean by Damped Oscillation? Explain the sharpness of resonance curve.

      `                                                                                                                                                                                   11107011

 

Short Questions

 

7.1: Name the two characteristics of SHM.

                                                                                    11107012

7.2: Does frequency depend on amplitude for harmonic oscillators?

                                                                                 11107013

7.3: Can we realize an ideal simple pendulum?                                                            11107014

7.4: What is the total distance traversed by an object moving with SHM in a time equal to its time period; if its amplitude is A?                                                                                         11107015

7.5: What happens to the period of simple pendulum if its length is doubled, What happens if the suspended mass is doubled?

                                                                            11107016

7.6: Does the acceleration of a simple harmonic oscillator remain constant during its motion? Is the acceleration ever zero? Explain.                                                            11107017

7.7 What is meant by phase angle? Does it define angle between maximum displacement and the driving force?

                        11107018

7.8: Under what conditions does the addition of two S.H.Ms produce a resultant, which is also simple Harmonic?

                           11107019

7.9: Show that in SHM the acceleration is zero when the velocity is greatest and velocity is zero when the acceleration is greatest?                                                                                11107020

7.10:    In relation to SHM, explain the equation.                                                                   11107021

(i)   y = A sin (wt + f)   (ii)        a = -w²x

7.11:    Explain the relation between total energy, potential energy and kinetic energy for a body oscillating with SHM.

                                                                        11107022

7.12:    Describe some common phenomena in which resonance plays an important role.                                                                                                 11107023

7.13: If a mass system is hung vertically and set into oscillations, why does the motion eventually stop?                                 11107024

 

Solved Examples

 

Example 1: A block weighing 4.0 kg extands a spring by 0.16m from its unstretched position. The block is removed and a 0.5 kg body is hung from the same spring. If the spring is now stretched and then released what is its period of vibration?                                                                      11107025

Example 2:      What should be the length of a simple pendulum whose period is 1.0 second at a place where g=9.8ms^-2? What is the frequency of such a pendulum?                            11107026

Example 3:      A spring whose spring constant is 80.0 Nm^-1 vertically supports a mass of 1.0 kg in the rest position. Find the distance by which the mass must be pulled down, so that on being released, it may pass the mean position with a velocity of 1.0 ms^-1                                                 11107027

Numericals Problems

 

 

 

7.1: A 100.0 g body hung on a spring, which elongates the spring by 4.0 cm. When a certain object is hung on the spring and set vibrating, its period is 0.568s. What is the mass of the object pulling the spring?                               11107028

Data:                                     

Mass of the body = m₁ = 100g = 0.1kg

Extension = x = 4 cm = 0.04 m

Time period = t = 0.568 s

          m₂ = ?

 

7.2: A load of 15.0 g elongates a spring by 2.00 cm. If body of mass 294 g is attached to the spring and is set into vibration with an amplitude of 10.0 cm, what will be its (i) period (ii) spring constant (iii) maximum speed of its vibration.                                  11107029

Data:  

Load=  m₁    = 15 g = 0.015 kg

Extension  =   x = 2 cm  = 0.02 m

Mass of the body = m₂ = 294 g = 0.294 kg

Amplitude = x_o = 10cm = 0.1m

Period =  T = ?

Spring constant =  k = ?

Maximum speed v₀ = ?

We know that

7.3: An 8.0 kg body executes SHM with amplitude 30 cm. The restoring force is 60 N when the displacement is 30 cm. Find.                      

(i)   Period

(ii)  Acceleration, speed, kinetic energy and potential energy when the displacement is 12 cm.                                      11107030

Data:

m = 8.0 kg                

x₀ = 30 cm or 0.3 m                 

x = 12 cm = 0.12 m

Period = T = ?

      Acceleration = a = ?

      Speed         v = ?

      K.E. = ?

      P.E. = ?

Displacement = x = 0.3 m                  

      Restoring force =  F_R = 60 N           

7.4: A block of mass 4.0 kg is dropped from a height of 0.80 m on to a spring of spring constant k=1960 Nm^-1, Find the maximum distance through which the spring will be compressed.                 

Date:                                                                       11107031

Mass of the block = m = 4.0 kg

      Height = h = 0.80 m

      Spring constant = k = 1960 N/m

      x = ?

7.5: A simple pendulum is 50.0 cm long. What will be its frequency of vibration at a place where g = 9.8 ms^-2?                          11107032

Data:  

Length of the simple pendulum =l = 50 cm

        = 0.5 m

g = 9.8 m/s²

f = ?

7.6: A block of mass 1.6 kg is attached to a spring with spring constant 1000 Nm^-1, as shown in Fig. The spring is compressed through a distance of 2.0 cm and the block is released from rest. Calculate the velocity of the block as it passes through the equilibrium position, x = 0, if the surface is frictionless.                                              11107033

Data:  

m = 1.6 kg = 1000 N/m

x₀ = 2 cm =

Velocity at mean position =  v₀ = ?

7.7: A car of mass 1300 kg is constructed using a frame supported by four springs. Each spring has spring constant 20,000 Nm^-1. If two people riding in the car have a combined mass of 160 kg, find the frequency of vibration of the car, when it is driven over a pot hole in the road. Assume the weight is evenly distributed.        11107034

Data:                          

Mass of car = m₁ = 1300 kg

      K for one spring = 20,000 Nm^-1

      K for 4 spring = 4 x 20,000 Nm^-1

      K = 80,000 Nm^-1

      Mass of persons = m₂ = 160 kg

      M = m₁ + m₂

7.8: Find the amplitude, frequency and period of an object vibrating at the end of a spring, if the equation for its position, as a function of time, is: x = 0.25 cos t What is the displacement of the object after 2.0 s?   

                                                                                    11107035

 

 

 

Unit 8

 

WAVES

 

 

Q.1 Define Wave. What are its type? Discuss.                                                                                     11108001

Q.2 What are mechanical waves? What are their types? Differentiate between longitudinal and transverse waves.                                                                                                                                                       11108002

Q.3 What are Periodic Waves? Establish relation between frequency (f), wavelength (l) and speed (v).                                                                                                                                                                     11108003

Q.4 How a phase difference between the two points on a wave is related with distance between them?                                                                                                                                                                 11108004

Q.5 Explain the propagation of sound wave in air and also derive Newton’s formula for the speed of sound.                                                                                                                                                       11108005

Q.6      What is Laplace Correction? How did Laplace corrected Newton derivation for the speed of sound?                                                                                                                                                             11108006

Q.7 What is the effect on the speed of sound with variation with (i)Pressure (ii)Density?

                                                                                                                                                                                          11108007

Q.8 Discuss the effect of the variation of temperature on the speed of sound in air and show that v_t = v_o + 0.61t.                                                                                                                                                            11108008

Q.9      Explain the superposition of waves.                                                                                    (Board 2008)    11108009

Q.10 Explain the interference of waves. What do you mean by constructive and destructive interference? Find their conditions in terms of path difference.       (Board 2009)      11108010

Q.11    What are Beats? How are they produced? Define beat frequency and show that beat frequency is the difference of frequency of two sound waves.                                                            11108011

Q.12  What do you mean by reflection of waves?                                                                                      11108012

Q.13  What are stationary waves? What are their characteristics?                                         11108013

Q.14  Explain the principle of quantization of frequency of waves.                OR                   11108014

Show that stationary waves in a stretched string has discrete value of frequency.

(Principle of quantization of frequency of transverse stationary waves).

Q.15 Explain the stationary waves set up in organ pipes. Discuss the various modes of vibration in organ pipe and find the expressions of frequency of different harmonics in (i) Closed end organ pipe (ii) Open end organ pipe.                                                                   11108015

Q.16 State and explain Doppler’s effect. Discuss its various cases and derive expression for modified frequency in each.                                                                                                                       11108016

Q.17  Describe various applications of Doppler’s effect.                                 (Board 2009,15) 11108017

Short Questions

 

8.1:         What features do longitudinal waves have in common with transverse waves?

                                                                            11108018

8.2: The five possible waveforms obtained, when the output from a microphone is fed into the Y-input of cathode ray oscilloscope, with the time base on, are shown in Fig 8.23. These waveforms are obtained under the same adjustment of the cathode ray oscilloscope controls. Indicate the waveform.                   

a)   Which trace represents the loudest note?

b)   Which trace represents the highest frequency?                                                     11108019

8.3: Is it possible for two identical waves traveling in the same direction along a string to give rise to a stationary wave.

                                                                        11108020

8.4: A wave is produced along a stretched string but some of its particles permanently show zero displacement. What type of wave is it?                            11108021

8.5: Explain the terms crest, trough, node and antinodes.        (Board 2010,15)  11108022

8.6: Why does sound travel faster in solids than in gases?                   (Board 2014)     11108023

8.7: How are beats useful in tuning musical instruments?  (Board 2010, 14) 11108024

8.8: When two notes of frequencies f₁ , and f₂ are sounded together, beats are formed f₁ > f₂. What will be the frequency of beats?                                                                           11108025

(i) f₁ + f₂                        (ii)  (f₁ + f₂)

(iii) f₁ - f₂                      (iv)  (f₁ - f₂)

8.9: As a result of distant explosion, an observer senses a ground tremor and then hears the explosion. Explain the time difference.                 (Board 2009,15) 11108026

8.10:    Explain why sound travels faster in warm air than in cold air?(Board 2014,15)11108027

8.11:    How should a sound source move with respect to an observer so that the frequency of its sound does not change?(

Board 2014) 11108028

 

Solved Examples

 

Example 1:      Find the temperature at which the velocity of sound in air is two times its velocity at 10 ^oC.                                                                                                                                                        11108029

Example 2:      A tuning fork A produces 4 beats per second with another tuning fork B. It is found that by loading B with some wax, the beat frequency increases to 6 beats per second. If the frequency of A is 320 Hz, determine the frequency of B when loaded.                           11108030

Example 3:      A steel wire hangs vertically from a fixed point, supporting a weight of 80 N at its lower end. The diameter of the wire is 0.50 mm and its length from the fixed point to the weight is 1.5 m. Calculate the fundamental frequency emitted by the wire when it is plucked?

(Density of steel wire = 7.8 x 10³ kgm^-3)                                                                                                                 11108031

Example 4:      A pipe has a length of 1 m. Determine the frequencies of the fundamental and the first two harmonics (a) if the pipe is open at both ends and (b) if the pipe is closed at one end. (Speed of sound in air = 340 ms^-1)                                                                                                                11108032

Example 5:      A train is approaching a station at 90 kmh^-1 sounding a whistle of frequency 1000 Hz. What will be the apparent frequency of the whistle as heard by a listener sitting on the platform? What will be the apparent frequency heard by the same listener if the train moves away from the station with the same speed?                                                                        11108033

(speed of sound = 340ms^-1)

Numericals

 

8.1.           The wavelength of the signals from a radio transmitter is 1500m and the frequency is 200KHz. What is the wavelength for a transmitter operating at 1000KHz and with what speed the radio waves travel.                                                      11108034

Data:

Frequency of the signal = f₁= 200KHz.

Wavelength of the signal =l₁ = 1500m

Frequency of transmitter =        f₂ = 1000KHz.

Wavelength of the transmitter    l₂ = ?

8.2.    Two speakers are arranged as shown in fig. the distance between them is 3m and they emit a constant tone of 344 Hz. A microphone ‘P’ is moved along a line parallel to and 4.00m from the line connecting the two speakers. It is found that tone of maximum loudness is heard and displayed on the CRO when microphone is on the centre of the line and directly opposite each speakers. Calculate the speed of sound.                                    11108035

Data:

      S₁P – S₂P = l

      f = 344Hz.

      S₁S₂ = 3m

      S₂P = 4m

8.3.    A stationary wave is established in a string, which is 120cm long and fixed at both ends. The string vibrates in four segments, at a frequency of 120Hz. Determine its wavelength and the fundamental frequency.

                        (Board 2015)     11108036

l = 120 cm = 1.2 m

Data:               l = 120cm  = 1.2m

         f₄ = 120Hz.

         n = 4

         l₄ = ?

         f₁ = ?

 

8.4 The frequency of the note emitted by a stretched string is 300 Hz. What is the frequency of this note when:                             

(a) Length of the wave is reduced by one third without changing tension,

(b) The tension is increase by one-third without changing the length of the wire.

                                                                                                11108037

8.5: An organ pipe has a length of 50cm. Find the frequency of its fundamental note and the next harmonic when it is:                      

(a) Open at both ends.

(b)  Closed at one end (speed of sound = 350m/s)                                                        11108038

Data:

n = 350m/s

      l = 50cm = 0.5m    

(a)  f₁ =?            When it is opened at

f₂ = ?  both ends.       

(b)  f₁ =?             When one end is closed

      f₂ = ?  other end is open

8.6: A church organ consists of pipes, each open at one end, of different lengths. The minimum length is 30mm and the longest is 4m. Calculate the frequency range of fundamental notes. (speed of sound= 340m/s).                                       (Board 2010)  11108039

Data:

l_min = 30mm =0.03m

      l_max = 4m.

      f_min = ?

      f_max = ?

           

8.7: Two tuning forks exhibit beats at a beat frequency of 3Hz. The frequency of one fork is 256Hz. Its frequency is then lowered slightly by adding a bit of wax to one of its prong. The two forks then exhibit a beat frequency of 1Hz. Determine the frequency of second tuning fork. 11108040

8.8 Two cars P and Q are Traveling along a motorway in the same direction. The leading car P travels at a steady speed of 12 m/s, the other car Q, traveling at a steady speed of 20 m/s, sound its horn to emit a steady note which P’s driver estimates has a frequency of 830 Hz. What frequency does Q’s own driver hear? (Speed of sound =   340 m/s).             11108041

Data:

n_P = 12 m/sec

n_Q = 20 m/s

f_C = 830 Hz

f  = ?

n  = 340 m/s

8.9: A train sounds its horn before it sets off from the station and an observer waiting on the platform estimates its frequency at 1200 Hz. The trains then moves off and accelerates steadily. Fifty seconds after departure, the deriver sounds the horn again and the platform observer estimates the frequency at 1140 Hz. Calculate the train speed 50 s after departure. How far from the station is the train after 50s?(Speed of sound=340 m/s).                               11108042

Date:

f = 1200 Hz

f_D = 1140 Hz

t = 50 sec

n_S = ?

Distance S = ?

8.10:    The absorption spectrum of faint galaxy is measured and the wavelength of one of the lines identified as the calcium line is found to be 478 nm. The same line has a wavelength of 397 nm when measured in a laboratory.                  

(a) Is the galaxy moving towards or away from the earth?

(b) Calculate the speed of the galaxy relative to Earth (Speed of light = 3.0 x 10⁸ ms^-1).                                                                11108043

Data:              

l_D =  478 nm

     =  478 x 10^-9 m

l   =  397 nm

     =  397 x 10^-9 m

c   =  3.0 x 10⁸ m/s

u_S =  ?

 

 

 

 

 

 

 

 

 

 

 

Unit 9

 

PHYSICAL OPTICS

 

 

 

Q.1 Define Physical Optics.                                                                                                                                   11109001

Q.2 Define wave front and explain it.                                                                                                        11109002

Q.3 What do you mean by Huygen’s principle? Also give its explanation and also define ray.

                                                                                                                                                                                          11109003

Q.4      What is the interference of light? Highlight the conditions of detectable interference.

                                                                                                                                                                                                            11109004

Q.5      Describe Young’s Double Slit experiment in detail. Discuss the theory of experiment and find expression for fringe width.                                                                                  (Board 2008)    11109005

Q.6  Explain interference in thin films. Why does thin film of soap exhibit colour when light falls on it?                                                                                                                                                            11109006

Q.7   What are Newton rings? How are they formed? Give an experimental detail of their formation.                                                                                                                           (Board 2007)       11109007

Q.8 Write a comprehensive note on Michelson Interferometer.                       (Board 2009,15)  11109008

Q.9      Define diffraction. Explain the diffraction of light.                                                               11109009

Q.10  Explain the diffraction of light through a narrow slit.                                                   11109010

Q.11    What is diffraction grating? Explain the diffraction of light by Grating and derive the grating equation of principle manimas.                                                                                          11109011

Q.12 Explain the diffraction of x-rays by crystal. Also derive the Bragg’s equation of x-ray diffraction. What are the uses of x-rays?                                                             (Board 2010)                         11109012

Q.13    Explain the Polarization of light. What do you mean by unpolarized and plane polarized light? Also discuss various methods of polarization.                                             11109013

Q.14 What do you mean by optical rotation?                                                                                      11109014

 

 

 

Short Questions

 

9.1:      Under what conditions two or more sources of light behave as coherent sources?                   (Board 2009, 10, 14) 11109015

9.2: How is the distance between interference fringes affected by the separation between the slits of Young’s experiment? Can fringes disappear?11109016

9.3: Can visible light produce interference fringes? Explain.                                       11109017

9.4: In the Young’s experiment, one of the slits is covered with blue filter and other with red filter. What would be the pattern of light intensity on the screen?           11109018

9.5: Explain whether the Young’s experiment is an experiment for studying interference or diffraction effects of light.

                                                       11109019

9.6: An oil film spreading over a wet footpath shows colours. Explain how does it happen?                (Board 2010,15)   11109020

9.7: Could you obtain Newton’s rings with transmitted light? If yes, would the pattern be different from that obtained with reflected lights?                  (Board 2014)  11109021

9.8: In the white light spectrum obtained with a diffraction grating, the third order image of a wavelength coincides with the fourth order image of a second wavelength. Calculate the ratio of the two wavelengths.                                               11109022

9.9: How would you manage to get more orders of spectra using a diffraction grating?                            (Board 2009,10)    11109023

9.10:    Why the Polaroid sunglasses are better than ordinary sunglasses?

                                    (Board 2009, 14,15) 11109024

9.11:    How would you distinguish between un-polarized and plane-polarized light?

                                    (Board 2014,15)              11109025

9.12:    Fill in the blanks.                                 11109026

(i).                 

 

Solved Examples

 

Example 1:      The distance between the slits in Young’s double slit experiment is 0.25 cm. Interference fringes are formed on a screen placed at a distance of 100 cm from the slits. The distance of the third dark fringe from the central bright fringe is 0.059 cm. Find the wavelength of the incident light.                                                                                                                      11109027

Example 2:      Yellow sodium light of wavelength 589 nm, emitted by a single source pass through two narrow slits 1.00 mm apart. The interference pattem is observed on a screen 225 cm away. How far apart are two adjacent bright fringes?                                                                11109028

Example 3:      Light of wavelength 450 nm is incident on a diffraction grating on which 5000 lines/cm have been ruled.                                                                                                                                             11109029

i)                   How many orders of spectra can be observed on either side of the direct beam?

ii)                 Determine the angle corresponding to each order.

 

Numerical Problems

 

9.1: Light of wavelength 546 nm is allowed to illuminate the slits of Young’s experiment. The separation between the slits is 0.10 mm and the distance of the screen from the slits where interference effects are observed is 20 cm. At what angle the first minimum will fall? What will be the linear distance on the screen between adjacent maxima?               11109030

Data:                         

l = 546 nm

l = 546 ´ 10^-9 m 

d = 0.10mm

d = 0.10 ´ 10^-3 m

L = 20cm = 20 ´ 10^-2 m

         = 0.2m

Angle for 1^st minimum = q  = ?

      Dy = ?

 9.2:     Calculate the wavelength of light, which illuminates two, slits 0.5 mm apart and produces an interference pattern on a screen placed 200 cm away from the slits. The first bright fringe is observed at a distance of 2.40 mm from the central bright image.                               (Board 2008)        11109031

9.3: In a double slit experiment the second order maximum occurs at q = 0.25^o. The wavelength is 650 nm. Determine the slit separation.                         (Board 2009,15)   11109032

Data:

l = 650 nm

q = 0.25^o

m = 2

            d = ?

9.4: A monochromatic light of l = 588 nm is allowed to fall on the half silvered glass plate G₁, in the Michelson Interferometer. If mirror M₁ is moved through 0.233 mm, how many fringes will be observed to shift?                                                        11109033

Data:

l = 588 nm ,

L = 0.233 mm  =  0.233 x 10 ^-3  m

m = ?

 

9.5: A second order spectrum is formed at an angle of 38.0^o when light falls normally on a diffraction grating having 5400 lines per centimeter. Determine wavelength of the light used.                                                     11109034

Data:  

m = 2, 

q = 38^o,         

N = 5400 lines per cm

      N = 540000 lines per meter 

l = ?

9.6: A light is incident normally on a grating, which has 2500 lines per centimeter. Compute the wavelength of a spectral line for which the deviation in second order is 15.0^o.                                11109035

Data:

N = 2500 lines per cm.

      N = 250000 lines per m.

m = 2,           

q = 15^o

      l = ?          

9.7: Sodium light (l = 589 nm) is incident normally on a grating having 3000 lines per centimeter. What is the highest order of the spectrum obtained with this grating?                                                                                        11109036

Data:

l = 589nm,  l = 589 x 10^-9 m

N= 3000 lines per cm

      N = 300000 lines per m.

      q = 90^o

      m = ?

9.8: Blue light of wavelength 480 nm illuminates a diffraction grating. The second order image is formed at an angle of 30^o from the central image. How many lines in a centimeter of the grating have been ruled?                                             11109037

Data:                          

l = 480nm,

l = 480 x 10^-9 m, 

q = 30^o,

m = 2,

      N = ?

9.9: X-rays of wavelength 0.150 nm are observed to undergo a first order reflection at a Bragg angle of 13.3^o from a quartz (SiO₂) crystal. What is the interplanar spacing of the reflecting planes in the crystal?                                  11109038

Data:

l = 0.150 nm

      l = 0.150 ´ 10^-9 m,

      q = 13.3^o

      n = 1

      d = ?                                         

9.10:    X-ray beam of wavelength l undergoes a first order reflection from a crystal when its angle of incidence to a crystal face is 26.5^o, and an X-ray beam of wavelength 0.197 nm undergoes a third order reflection when its angle of incidence to that face is 60.0^o. Assuming that the two beams reflect from the same family of planes, calculate

 (a) the interplanar spacing of the planes and (b) the wavelength l.                11109039

Data:

For first wave length l₁ 

q₁ = 26.5^o

For first order reflection n₁ = 1

For second wave length l₂  = 60^o 

Wavelength of 2^nd beam l₂  = 0.097 nm = 0.097 x 10^-9 m

For third order reflection = n₂  = 3

Interplaner spacing = d = ?

Wavelength of 1^st beam =          l₁  = ?

 

 

 

 

 

Unit 10

 

OPTICAL INSTRUMENTS

 

 

 

 

Q.1 What are the optical instruments?                                                                                                      11110001

Q.2 Define the following:                                                                                                                                       11110002

(i) Least distance of distinct vision (ii) Magnifying Power (iii) Visual Angle

Q.3 What is meant by angular magnification and resolving process?                          11110003

Q.4   Explain how a convex lens act like a simple microscope. Draw it ray diagram and find an expression for its magnifying power.                                                                                             11110004

Q.5   Describe compound microscope. Draw its ray diagram and obtain an expression for its magnifying power.                                                                                                    (Board 2015)     11110005

Q.6 Describe an astronomical telescope, draw its ray diagram and explain its working. What is meant by its normal adjustment? Obtain the expression for its magnifying power. 11110006

Q.7 Write a comprehensive note on spectrometer. Also write about its uses.               11110007

Q.8 Describe an experimental detail of Michelson method for determination of speed of light.                                                                                                                                                                                     11110008

Q.9 What is fiber optic? Discuss its advantages.                                                                                        11110009

Q.10    Explain the fiber optic principle for the following:                                                                  11110010

(i) Total Internal Reflection              (ii) Continuous Refraction.

Q.11 Describe different types of optical fibers.                        OR

How many types of optical fibers are there? Discuss them.                                                  11110011

Q.12    Explain the working of fiber optic communication system, also discuss the causes due to which power is lost in optical fiber.                                                                                         11110012

 

 

Short Question

 

Q.10.1 What do you understand by linear magnification and angular magnification? Explain how a convex lens is used as a magnifier?                   (Board 2009,10) 11110013

Q.10.2 Explain the difference between angular magnification and resolving power of an optical instrument. What limits the magnification of an optical instrument?             (Board 2014)     11110014

Q.10.3: Why would it be advantageous to use blue light with a compound microscope?              (Board 2010, 14,15)  11110015

Q.10.4. One can buy a cheap microscope for use by the children. The images seen in such a microscope have coloured edges. Why is this so?                                         11110016

Q.10.5 Describe with the help of diagram, how (a) single biconvex lens can be used as a magnifying glass (b) biconvex lens can be arranged to form a microscope. 11110017

Q.10.6 If a person was looking through a telescope at the full moon. How would the appearance of the moon be changed by covering half of the objective lens?

                                                                (Board 2010)  11110018

Q.10.7 A magnifying glass gives a five times enlarged image at a distance of 25 cm from the lens. Find, by ray diagram, the focal length of the lens.                                      11110019

Q.10.8: Identify the correct answer. 11110020

(i)   The resolving power of a compound microscope depends on;      

a.   Length of the microscope.

b.   The diameter of objective lens.

c.   The diameter of the eyepiece.

d.   The position of an observer’s eye with regard to the eye lens.

Q.10.9: Draw sketches showing the different light paths through a single-mode and a multi-mode fibre. Why is the single-mode fibre is preferred in telecommunications?

                                                                        11110021

Q.10.10: How the light signal is transmitted through the optical fibre?               11110022

Q.10.11: How the power is lost in optical fibre through dispersion? Explain. 11110023

 

Solved Examples

Example 1:      A microscope has an objective lens of 10 mm focal length, and an eye piece of 25.0 mm focal length. What is the distance between the lenses and its magnification, if the object is in sharp focus when it is 10.5 mm from the objective?                                                           11110024

Example 2:      Calculate the critical angle and angle of entry for an optical fibre having core of refractive index 1.50 and cladding of refractive index 1.48.                                                11110025

Numerical

Q10.1 A converging lens of focal length 5.00cm is used as a magnifying glass. If the near point of the observer is 25cm and the lens is held close to the eye. calculate (i) the distance of the object from the lens. (ii) The angular magnification. What is the angular magnification when the final image is formed at infinity?         11110026

Data:

Focal length = f = 5cm

Near point = d = q  =  -25cm  (image is virtual)

Distance of the object form the lens= p= ?

Angular magnification= M=?

Angular magnification when image is at infinity?

(i) p  =  ?

10.2: A telescope objective has focal length 96 cm and diameter 12 cm. Calculate the focal length and minimum diameter of a simple eye piece lens for use with the telescope, if the linear magnification required is 24 times and all the light transmitted by the objective from a distant point on the telescope axis is to fall on the eye piece.                                               11110027

10.3: A telescope is made of an objective of focal length 20 cm and an eye piece of 5.0 cm, both are convex lenses. Find the angular magnification.                            11110028

Data:  

Focal length of objective =   f_o = 20cm,  

Focal length of eye piece =  f_e = 5cm

Angular magnification = M = ?

10.4: A simple astronomical telescope in normal adjustment has an objective of focal length 100 cm and an eye piece of focal length 5.0 cm. (i) Where is the final image formed? (ii) Calculate the angular magnification.                                    11110029

Data:

Focal length of objective = f_o = 100cm   

Focal length of eye piece  f_e = 5cm

i. Distance of the final image = q = ?

ii. Angular Magnification = M = ?         

10.5: A point object is placed on the axis of 3.6 cm from a thin convex lens of focal length 3.0 cm. A second thin convex lens of focal length 16.0 cm is placed coaxial with the first and 26.0 cm from it on the side away from the object. Find the position of the final image produced by the two lenses.

Data:                                                               11110030

Distance of object = p₁ = 3.6cm

Focal length of 1^st Lens = f₁=     3.0cm  

Focal length of 2^nd Lens = f₂       = 16.0 cm

Distance between the two lenses = L = 26cm

Position of final image = q₂ = ?

Image formed by the objective = q₁

10.6: A compound microscope has lenses of focal length 1.0 cm and 3.0 cm. An object is placed 1.2 cm from the object lens. If a virtual image is formed, 25 cm from the eye, calculate the separation of the lenses and the magnification of the instrument.                                    (Board 2010)  11110031

Data:

Focal length of objective= f_o = 1cm,     

Focal length of eye piece = f_e = 3cm, 

Distance of object form objective = p₁

        = 1.2cm

Distance of final image = q₂ = -25cm (virtual image)

p₂= ?

Separation of lenses = L = ?

Magnification = M = ?

10.7: Sodium light of wavelength 589 nm is used to view an object under a microscope. If the aperture of the objective is 0.90 cm, (i) find the limiting angle of resolution, (ii) using visible light of any wavelength, what is the maximum limit of resolution for this microscope.                                                                       11110032

Date:

(a).    l = 589nm = 589 ´ 10^-9m

      D = 0.09 cm = 0.90 ´ 10^-2m

      µ_min = ?

10.8: An astronomical telescope having magnifying power of 5 consist of two thin lenses 24 cm apart. Find the focal lengths of the lenses.                      (Board 2015)         11110033

Data:                          

M = 5,

      L = 24 cm

      f_o = ?

      f_e = ?

10.9: A glass light pipe in air will totally internally reflect a light ray if its angle of incidence is at least 39^o. What is the minimum angle for total internal reflection if pipe is in water? (Refractive Index of water = 1.33).                                                    11110034

Date:

Angle of incidence for glass = q_c = 39^o   (for air-glass)

Angle of incidence of water = q₁ = ?

10.10: The refractive index of the core and cladding of an optical fibre are 1.6 and 1.4 respectively. Calculate (i) the critical angle for the interface (ii) the maximum angle of incidence in the air, of a ray, which enters the fibre and is incident at the critical angle on the interface.                          11110035

 

Unit 11

HEAT AND THERMODYNAMICS

 

 

Q.1 Describe the fundamental postulates of the kinetic theory of gases.                                  11111001

Kinetic theory of gases:

Q.2 Using kinetic theory of gases, prove the following relations:                     (Board 2009) 11111002

      (i) P =  r < v² >                (ii)  p  < K . E >                                (iii) T  <  mv² >

Q.3      Deduce the Boyle’s law and Charles’ Law from kinetic theory of gases.                     11111003

Derivation of gas laws from kinetic theory of gasses:

Q.4   Define the term “internal energy”. Show that internal energy is a function of state and is independent of paths.                                                                                                                                          11111004

Q.5 Describe transfer of energy into work and heat. Calculate the work done by a thermodynamic system.                                                                                                                                            11111005

Q.6 State and explain first law of thermodynamics.                                                                            11111006

1^st Law of Thermodynamics:

Q.7 Discuss the applications of 1^st law of thermodynamics. OR

Discuss the following processes and draw P – V diagram in each case.                     11111007

(i)                 Isothermal process                     (ii) Adiabatic process

Q.8 Define molar specific heats of a gas. Also prove that C_p – C_v = R. OR                  11111008

      Show that difference between two specific heats of a gas is equal to molar gas constant.

Q.9 Describe reversible and irreversible processes.                                                                             11111009

Q.10 What is heat engine? What is its principle?                                                                                      11111010

Q.11 State and explain second law of thermodynamics.                                                                      11111011

Q.12 What is Carnot engine? Describe the Construction, principle and working of Carnot engine. Derive the expression for the efficiency of Carnot engine. Also state Carnot theorem.

                                                                                          11111012

Q.13 Describe thermodynamic scale of temperature.                                                                          11111013

Q.14 What is meant of triple point?                                                                                                          11111014

Q.15 Describe the principle, construction and working of petrol engine.        (Board 2008)    11111015

Q.16 Discuss diesel engine in detail.                                                                                        (Board 2008)11111016

Q.17  What is entropy? Explain it.                                                                                                                        11111017

Q.18 Explain second law of thermodynamics in terms of entropy.                                          11111018

Q.19 Increase in entropy means degradation of energy. Discuss.                                                        11111019

Q.20 How environmental crisis are related with entropy crisis.                                                          11111020

Short Questions

11.1          Why is the average velocity of the molecules of a gas zero but the average of square of velocities is not zero.

(Board 2010,15)      11111021

11.2           Why does the pressure of a gas in a car tyre increase when it is driven through some distance?            (Board 2014)     11111022

11.3           A system undergoes from state P₁V₁ to state P₂V₂ as shown in fig. What will be the change in internal energy?           11111023

11.4     Variation of volume by pressure is given in fig. A gas is taken along the paths ABCDA, ABCA and A to A what will be the change in internal energy?                     11111024

 

11.5         Specific heat of a gas at constant pressure is greater than specific heat at constant volume. Why?

                                                (Board 2010, 14) 11111025

11.6         Give an example of a process in which no heat is transferred to or from the system but the temperature of the system changes.                                         (Board 2009)  11111026

11.7         Is it possible to convert internal energy into mechanical energy? Explain with an example.                   (Board 2014)  11111027

11.8         Is it possible to construct a heat engine that will not expel heat into the atmosphere?             (Board 2010,15) 11111028

11.9     A thermos flask containing milk as a system is shaken rapidly. Does the temperature of milk rise?(Board 2015)11111029

11.10 What happens to the temperature of the room, when air conditioner is left running on a table in the middle of the room?                                               (Board 2009) 11111030

11.11 Can the mechanical energy be converted completely into heat energy? If, so give an example? (Board 2008) 11111031

11.12 Does entropy of a system increase or decrease due to friction? (Board 2014) 11111032

11.13   Give an example of a natural process that involves an increase in entropy.                              (Board 2009)            11111033

11.14  An adiabatic change is the one in which?                                                                                          11111034

(a)    No heat is added to or taken out of the system.

(b)  No change of temperature takes place.

(c)  Boyle’s law is applicable.

(d)  Pressure and Volume remain constant.

11.15  Which one of the following process is irreversible?                                                                       11111035

(a)  Slow compression of an elastic spring.

(b)    Slow evaporation for a substance in a isolated vessel.

(c)  Slow compression of a gas.

(d)  A chemical explosion. 

11.16  An ideal reversible heat engine has

                                                                              11111036

(a)  100% efficiency.

(b)  Highest efficiency.

(c)    An efficiency which depends on the nature of working substance. 

(d)  None of these.

 

 

Solved Examples

 

Example 1:      What is the average translational Kinetic energy of molecules in a gas at temperature 27C^o?                                                                                                                                                       11111037

Example 2:      Find the average speed of oxygen molecule in the air at S.T.P.                       11111038

Example 3:      A gas is enclosed in a container fitted with a piston of cross-sectional area 0.10 m². The pressure of the gas is maintained at 8000 Nm^-2. When heat is slowly transferred, the piston is pushed up through a distance of 4.0 cm. If 42 J heat is transferred to the system during the expansion, what is the change in internal energy of the system?                   11111039

Example 4:      The turbine in a steam power plant takes steam from a boiler at 427^oC and exhausts into a low temperature reservoir at 77^oC. What is the maximum possible efficiency?

11111040

Example 5:      Calculate the entropy change when 1.0 kg ice at 0^oC melts into water at 0^oC. Latent heat of fusion of ice L_f = 3.36 ´ 10⁵ J kg^-1.                                                                                    11111041

 

Numerical

 

11.1          Estimate the average speed of nitrogen molecules in air under standard conditions of pressure and temperature.

Data:                                                               11111042

      T = 0^oC + 273 = 273K

      k = 1.38 ´ 10^-23 J/K

      Molecular Weight of N₂ = 28

      Root mean square velocity. v_rms = ?

11.2     Show that ratio of the root mean square speeds of molecules of two different gases at a certain temperature is equal to the square root of the inverse ratio of their masses.                                                            11111043

11.3     A sample of gas is compressed to one half of its initial volume at constant pressure of 1.25 x 10⁵Nm^-2. During the compressions, 100 J of work is done on the gas. Determine the final volume of gas.   

Data:                                                               11111044

      Let the initial volume = V₁

      Final Volume        V₂ = V₁

\   V₁ = 2V₂

      P = 1.25 ´ 10⁵ N/m²

      W = -100 J

\     V₂ = ?

11.4          A thermodynamic system undergoes a process in which its internal energy decreases by 300J. If at the same time 120J of work is done on the system, find the heat lost by the system.                               11111045

Data:

      DU = -300 J

      W = -120 J

      Q = ?

11.5          A Carnot engine utilize an ideal gas. The source temperature is 227^oC and the sink temperature is 127^oC. Find the efficiency of the engine. Also find the heat input from the source and heat rejected to the sink when 10000J of work is done.

Data:                           (Board 2010)       11111046

T₁ = 227°C = 227 + 273 = 500 K

T₂ = 127°C = 127 + 273 = 400 K

W = 10000 J

h = ?

Q₁ = ?

Q₂ = ?

11.6          A reversible engine works between two temperatures whose difference is 100^oC. If it absorbs 746J of heat from the source and rejects 546J to the sink, calculate the temperature of the source and the sink. 

Data:                                                               11111047

      Q₁ = 746 J

      Q₂ = 547 J

      (T₁ - T₂) = rT = 100

      T₁ = ?

      T₂ = ?

11.7           A mechanical engineer develops an engine, working between 327^oC and 27^oC and claim to have an efficiency of 52%. Does he claim correctly? Explain.    11111048

Data:                                                   (Board 2015)

      T₁ = 327°C = 327 + 273 = 600 K

      T₂ = 27°C = 27 + 273 = 300 K

      h = ?

11.8          A heat engine performs 100 J of work and at the same time rejects 400J of heat energy to the cold reservoir. What is the efficiency of the engine?      (Board 2014) 11111049

Data:

      W = 100 J

      Q₂ = 400 J

      h = ?

11.9:    A carnot engine whose low temperature reservoir is at 7^oC has an efficiency of 50%. It is desired to increase the efficiency to 70%. By how many degrees the temperature of the source be increased?                                                     11111050

Data:                                                  

      h₁ = 50%

      h₂ = 70%

      T₂ = 7^oC = 7 + 273 = 280 K

      rT = ?

11.10 A steam engine has a boiler that operates at 450K. The heat changes water into steam, which drives the piston. The exhaust temperature of the outside air is about 300K. What is the maximum efficiency of the steam engine?                       11111051

Data: 

      T₁ = 450 K

      T₂ = 300 K

11.11 336J of energy is required to melt 1g of ice at 0^oC. What is the change in entropy of 30g of water at 0^oC as it is changed to ice at 0^oC by a refrigerator?

Data:                           (Board 2009,15)  11111052

      m = 30 g

      L_f = 336 J/gm

      T = 0°C = 0 + 273 = 273 K

      rS = ?