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ITL Public School

Annual Examination (2013-14)

Physics(042) (Set -A)

Date: 11.02.15 ANSWER KEY Class: XI

Time:3 hrs M. M: 70

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.

Ans- 300

1

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

Ans- √

1

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

Ans- ∑

1

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

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

Ans-

)

1

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

Ans- to hear distinct beats time interval between two successive beats must be greater

than

second.

1

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).

Ans-volume of bigger drop = volume of 1000 small drops

r=2 × 10-4

m 1

change in surface energy = 3168 10-8

J 1 ½

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 kinetic energy? Explain.

Ans- KE of A =

KE of B =

1

KE of B > KE of A 1

2

8 Find the dimensions of a×b in the relation

; Where is power, is distance and

is time.

Ans- [B] = [L2] [a] = [ML

5T

-2] 1

2

9 To a driver going 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?

Ans- VB= 80 Km/hr. 1

tan β =

√ 1

2

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

Ans- Statement 1

Proof 1

OR

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

Ans- conservative- work done is independent of path. eg-gravitational force ½ + ½

non conservative force-work done path dependent eg-frictional ½ + ½

2

Section- C

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

Ans- Statement 1+1

(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’?

Ans- I=Icom+ Mr2 =

1

3

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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.

Ans- bob released with zero velocity ½

mv

2 1

v= √

1

= 6 m/s ½

3

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

Ans- Derivation 3

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.

Ans- Derivation 3

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?

Ans- T1-mg =ma ½

2mg – T1 =2ma ½

mg-T2= ma ½

a=

½

T1=

½

T2=

½

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?

Ans- Derivation 2

√

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?

Ans- v = √

~ 280 m/s 1

Laplace said sound propagation –adiabatic process 1

v=√

1 OR

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

Ans- a uniform circular motion projected along any diameter represents a SHM. 1

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

waves.

Ans-

=

2

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.

Ans- Definition ½

Derivation 1 ½

In a capillary tube of insufficient height, the liquid rises to the top and spreads out to a

new radius of curvature but the liquid will not overflow 1

3

19 i. Derive an expression for the orbital velocity of a satellite. 3

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Ans-Derivation 2

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

related with velocity of escape from that planet?

Ans- ve=√ V0 1

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

Ans- Definition 1

Derivation 2

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.

Ans- Statement 1

(i) U =

γ =5/3 ½

(ii) U=

γ = 7/5 ½

(iii) Linear - U=

= 9/7 ½

non linear U = 3RT γ = 4/3 ½

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.

Ans- a= )

1

velocity of ball on reaching surface v2= 2as = 2

– )

2

H= (

) 1

3

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.

Ans- (i) Kavita is very understanding and helpful .

(ii) 144.35 km/h

(iii) 20 π rad./s

4

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?

Ans- (a) Definition ½

trajectory 1

Max height ½

time of flight ½

horizontal range ½

(b)

2 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

5

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banked curve.

Ans- (a) Definition ½

Derivation 1½

(b) Derivation 3

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 × 105 Jkg

-1)

Ans- (a) Principle 1

construction & working coefficient of

performance 2

(b) W= 2.092 × 104 J 2

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.

Ans- (a) 600 K (b)1500 R, 831.6 R, -900 R, -830.6 R (c) W=600 R 1+3+1

5

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

Ans- (I) Doppler effect 1

Derivation 2

(II) (i)(a)412.12Hz (b) 388.5Hz 1 ½

(II) 340m/s ½

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.

Ans- (I) Derivation (2)

(II) (a) Stationary wave 1

(b) 3m,180m/s,60Hz 1 ½

(c) 648N ½

5

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