XI A 1 of 3

ITL Public School

Annual examination (2014-15)

Date: 11.02.15 Class: XI Physics(042) (Set -A)

Time:3 hrs M. M: 70 General Instructions:

1. All questions are compulsory. There are 26 questions in all. 2. This question paper has five sections. 3. Section A contains five questions of one mark each, Section B contains five questions of two

marks each, Section C contains twelve questions of three marks each, Section D contains one value based question of four marks and Section E contains three questions of five marks each.

4. There is no overall choice. However, an internal choice has been provided in one question of two marks, one question of three marks and all three questions of five marks each. You have to attempt only one of the given choices in such questions.

Section - A

1 A cubical block rests on an inclined plane of coefficient of friction 1/√ . Determine the angle of

inclination when the block just slides down the inclined plane.

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2 What condition is to be satisfied for a mass tied to a string to perform a vertical circle?

1

3 What is analogous to Newton’s second law of motion in rotational motion?

1

4 Write equation of S.H.M. having following characteristics:

Amplitude = 0.05 m, frequency = 50 Hz, initial phase =

1

5 Why should the difference between the frequencies be less than 10 Hz to produce beats?

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Section – B

6 A liquid drop of diameter of 4 mm breaks into 1000 droplets of equal size. Calculate the resultant

change in energy (the surface tension of liquid is 0.07 N/m).

2

7 The moment of inertia of two rolling bodies A and B are IA and IB (IA > IB) and their angular

momenta are equal. Which one has greater rotational kinetic energy? Explain.

2

8 Find the dimensions of a×b in the relation

; Where is power, is distance and is time.

2

9 To a driver going east in a car with a velocity of 40 Km/h, a bus appears to move towards north

with a velocity of √ km/h. What is the actual velocity and direction of motion of the bus?

2

10 State and prove work energy theorem for a variable force.

OR

Distinguish between conservative and non-conservative forces with one example each.

2

Section- C

11 (i) State parallel-axes and perpendicular axes theorem.

(ii) What is the moment of inertia about an axis passing through the edge as a tangent in the plane

of a disc of mass M and radius ‘r’?

3

12 The string of a pendulum is 2.0 m long. The body is pulled sideways so that the string becomes

horizontal and bob is released. What is the speed with which the bob is released? What is the speed

which the bob arrives at the lowest point? Assume that 10% of the initial energy is used against air

resistance.

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XI A 2 of 3

13 On the basis of kinetic theory, derive an expression for pressure exerted by an ideal gas.

3

14 A liquid is in a streamline flow through a pipe of non-uniform cross-section. Prove that the sum of

its kinetic energy, pressure energy and potential energy per unit volume remains constant.

3

15 Three bodies A, B and C each of mass m are hanging on a string over a fixed pulley, as shown in

fig. What are the tensions in the strings connecting bodies A to B and B to C?

3

16 Derive an expression for variation of acceleration due to gravity with depth below the earth’s

surface. A Simple pendulum has a time period T1 when on the earth’s surface, and T2 when taken

to a depth R/4 below the earth’s surface, where R is the radius of earth. What is the valve of T2/T1?

3

17 Write Newton’s formula for the speed of sound in air. What was wrong with this formula? What

correction was made by Laplace in this formula?

OR

i. What is geometrical meaning of S.H.M.?

ii. If y1= 5cos ωt and y2= 5 [ √ cos ωt + sin ωt], find the ratio of the amplitudes of two waves.

3

18 What is capillarity? Derive an expression for the height to which the liquid rise in the capillary

tube of radius r. Explain What happens when the length of a capillary tube is less than the height

upto which the liquid may rise in it.

3

19 i. Derive an expression for the orbital velocity of a satellite.

ii. A satellite revolves close to the surface of a planet. How is its orbital velocity related with

velocity of escape from that planet?

3

20 What is a progressive wave? Derive an equation for a plane progressive harmonic wave.

3

21 State the law of equipartition of energy of a dynamic system and use it to find the values of internal

energy and the ratio of the specific heats of a (i) monatomic (ii) diatomic and (iii) triatomic gas

molecules.

3

22 A wooden ball of density ρ is immersed in water of density σ to depth h and then released. Find the

height H above the surface of water upto which the ball jumps out of water.

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Section D

23 Meenu was afraid of going anywhere by air. Once, she couldn’t avoid going by an aeroplane. Her

friend Kavita, who knew her problem, was with her. Inside the plane, Kavita saw that Meenu was

very quiet and feeling uncomfortable. She tried to talk to Meenu but she didn’t answer. As the

plane was about to take off, Kavita started fighting with Meenu without any cause for diverting her

mind. While flighting, Meenu didn’t realize that plane had taken off and now she was in air. She

felt very happy to overcome her fear.

i. What values do you associate with Kavita?

ii. An aeroplane takes off at an angle of 300 to the horizontal. If the component of its velocity

along the horizontal is 250 km/h. What is its actual velocity? Find also the vertical

component of velocity.

iii. The blades of an aeroplane propeller are rotating at the rate of 600 revolutions per minute.

Calculate its angular velocity.

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XI A 3 of 3

Section E

24 (a) What is projectile? Derive the expression for the trajectory, maximum height, time of flight, and

horizontal range for a projectile thrown upward, making an angle θ with the horizontal direction.

(b) What will be the effect on maximum height of a projectile when its angle of projection is

changed from 300 to 60

0, keeping the same initial velocity of projection?

OR

(a) What is centripetal acceleration? Find its magnitude and direction in case of uniform circular

motion.

(b) Derive a relation for the optimum velocity of negotiating a curve by a body in a banked curve.

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25

(a)What is the principle of a heat pump? Explain the working of a heat pump with a block diagram

and obtain an expression for its coefficient of performance.

(b) Assuming that a domestic refrigerator can be regarded as a reversible engine working between

the temperature of melting ice and that of atmosphere (17oC), calculate the energy which must be

supplied to freeze one kilogram of water already at 0o C.( latent heat of fusion of ice = 3.3 × 10

5

Jkg-1

)

OR

A monatomic ideal gas of two moles is taken through a cyclic

process starting from A as shown in fig. The volume ratios

are

and

. If the temperature TA at A is 27

0C ,

calculate,

(a) the temperature of the gas at a points B,

(b) heat absorbed or released by the gas in each process

(c) the total work done by the gas during the complete cycle.

mention your answer in terms of the gas constant R.

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26

(I) What is Doppler’s effect of sound? Obtain an expression for apparent frequency of sound when

source and listener are approaching each other in a moving medium.

(II) A train, standing at the outer signal of a railway station blows a whistle of frequency

400 Hz in still air. (i) What is the frequency of the whistle for a platform observer

when the train (a) approaches the platform with a speed of 10 m s–1

, (b) recedes

from the platform with a speed of 10 m s–1? (ii) What is the speed of sound in each

case? The speed of sound in still air can be taken as 340 m s–1

OR

(I) Prove analytically that in the case of a closed organ pipe of length L, the frequencies of the

vibrating air column are given by ( )

(II) The transverse displacement of a string (clamped at its both ends) is given by

( ) (

) ( )

Where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3× 10–2

kg.

Answer the following :

(a) Does the function represent a travelling wave or a stationary wave?

(b) Interpret the wave as a superposition of two waves travelling in opposite directions.What is the

wavelength, frequency, and speed of each wave?

(c) Determine the tension in the string.

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