#### 11th Half Yearly Model Question

11th Standard

Reg.No. :
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Physics

Time : 02:30:00 Hrs
Total Marks : 70
I. Choose the most suitable answer:
15 x 1 = 15
1. The dimension of ${\left( {\mu}_{0}{\epsilon}_{0} \right)}^{{{1}\over{2}}}$ is

(a)

length

(b)

time

(c)

velocity

(d)

force

2. If a particle executes uniform circular motion in the xy plane in clock wise direction, then the angular velocity is in

(a)

+y direction

(b)

+z direction

(c)

-z direction

(d)

-x direction

3. Choose the motion in two dimension from the following.

(a)

Motion of a train along a straight railway track

(b)

An object falling freely under gravity close to the Earth.

(c)

A particle moving along a curved path in a plane.

(d)

Flying ofa kite on a windy day.

4. A vehicle is moving along the positive x direction, if sudden brake is applied, then

(a)

frictional force acting on the vehicle is along negative x direction

(b)

frictional force acting on the vehicle is along positive x direction

(c)

no frictional force acts on the vehicle

(d)

frictional force acts in downward direction

5. A uniform force of (2$\hat { i }$+$\hat { j }$) N acts on a particle of mass 1 kg. The particle displaces from position (3$\hat { j }$+$\hat { k }$) m to (5$\hat { i }$+3$\hat { j }$) m. The work done by the force on the particle is

(a)

9 J

(b)

6 J

(c)

10 J

(d)

12 J

6. The speed of the center of a wheel rolling on a horizontal surface is vo  A point on the rim in level with the center will be moving at a speed of

(a)

zero

(b)

vo

(c)

$\sqrt{2}$vo

(d)

2vo

7. In a rectangle ABCD (BC = 2AB). The moment of inertia is minimum along axis through

(a)

BC

(b)

BD

(c)

HF

(d)

EG

8. In the following, what are the quantities which that are conserved?

(a)

Linear momentum of planet

(b)

Angular momentum of planet

(c)

Total energy of planet

(d)

Potential energy of a planet

9. The wettability of a surface by a liquid depends primarily on

(a)

viscosity

(b)

surface tension

(c)

density

(d)

angle of contact between the surface and the liquid

10. A pure substance would freeze or solidity at its

(a)

boiling point

(b)

condensation point

(c)

melting point

(d)

sublimation point

11. An ideal refrigerator has a freezer at temperature −12°C. The coefficient of performance of the engine is 5. The temperature of the air (to which the heat ejected) is

(a)

50°C

(b)

45.2°C

(c)

40.2°C

(d)

37.5°C

12. If sP and sV denote the specific heats of nitrogen gas per unit mass at constant pressure and constant volume respectively, then

(a)

sP - sV = 28R

(b)

sP - sV = R/28

(c)

sP - sV = R/14

(d)

sP - sV = R

13. A pendulum is hung in a very high building oscillates to and fro motion freely like a simple harmonic oscillator. If the acceleration of the bob is 16 ms−2 at a distance of 4 m from the mean position, then the time period is

(a)

2 s

(b)

1 s

(c)

2$\pi$s

(d)

$\pi$s

14. The ratio of frequences of 2 pendulums are 2 : 3, then their lengths are in ratio,

(a)

$\sqrt { \frac { 2 }{ 3 } }$

(b)

$\sqrt { \frac { 3 }{ 2 } }$

(c)

$\frac{4}{9}$

(d)

$\frac{9}{4}$

15. Let y=$\frac{1}{1+x^2}$ at t = 0 s be the amplitude of the wave propagating in the positive x-direction. At t = 2 s, the amplitude of the wave propagating becomes

(a)

0.5m s-1

(b)

1.0m s-1

(c)

1.5m s-1

(d)

2.0m s-1

16. II. Answer any six questions. Q.No 18 is compulsory:
6 x 2 = 12
17. Is it possible to have length and velocity both as fundamental quantities? Why

18. A train 100 m long is moving with a speed of 60 km h-1. In how many seconds will it cross a bridge of 1 km long?

19. Why it is not possible to push a car from inside?

20. A man pulls a lawn roller through a distance of 20 m with a force of 20 kg weight. If he applies the force at an angle of 60° with the ground, calculate the power developed if he takes 1 min in doing so.

21. When a tree is cut, the cut is made on the side facing the direction in which the tree is required to fall. Why?

22. Write down the expression for the Stoke’s force and explain the symbols involved in it.

23. A man starts bicycling in the morning at a temperature around 25°C, he checked the pressure of tire which is equal to be 500 kPa. Afternoon he found that the absolute pressure in the tyre is increased to 520 kPa. By assuming the expansion of tyre is negligible, what is the temperature of tyre at afternoon?

24. What is meant by force constant of a spring?.

25. What is persistence of hearing?

26. III. Answer any six questions. Q. No 33 is compulsory:

6 x 3 = 18
27. Give any three practical units of time.

28. What is non uniform circular motion?

29. A block of mass m is pushed momentarily along a horizontal surface with an initial velocity u. If uk is the coefficient of kinetic friction between the object and surface, find the time at which the block comes to rest.

30. What is meant by negative work? Give example.

31. Write the equation for the CM of two point masses when, (i) Masses are on positive x-axis. (ii) Origin coincides with anyone of the masses, (iii) origin coincides with CM itself.

32. Draw graphs showing the variation of acceleration due to gravity with (i) height above the earth's surface (ii) depth below the earth's surface.

33. A metal tube & a rod of same distance, same material & same outer diameter are given same amount of heat. Which will show less expansion & why?

34. Equal masses of O2 and He gases are supplied equal amount of heat. Which gas will undergo a greater temperature rise and why?

35. Calculate the speed of sound in a steel rod whose Young’s modulus Y = 2 × 1011 N m-2 and $\rho$ = 7800 kg m-3.

36. IV. Answer all in detail
7 x 5 = 35
1. Check the correctness of the equation$\frac { 1 }{ 2 }$mv2 = mgh using dimensional analysis method.

2. Derive the kinematic equations of motion for constant acceleration.

1. Write note on integration.

2. Consider a circular leveled road of radius 10m having coefficient of static friction 0.81. Three cars (A, B and C) are travelling with speed 7 ms-1, 8m s-1 and 10 ms-1 respectively. Which car will skid when it moves in the circular level road? (g = 10 m s-2).

1. A shot travelling at the rate of 100 ms-1 is just able to pierce a plank 4cm thick. What velocity is required to just pierce a plank 9cm thick?

2. Explain the types of equilibrium with suitable examples:

1. Derive an expression for kinetic energy in rotation and establish the relation between rotational kinetic energy and angular momentum.

2. Consider two point masses m1 and m2 which are separated by a distance of 10 meter as shown in the following figure. Calculate the force of attraction between them and draw the directions of forces on each of them. Take m1= 1 kg and m2 = 2 kg

1. Obtain an equation of continuity for a flow of fluid on the basis of conservation of mass.

2. Explain in detail Newton’s law of cooling.

1. Motor volume is occupied 1 moleof any (ideal) gas at standard temperature and pressure. Show that it is 22.4 litres.

2. Which of the following represent simple
harmonic motion?
(i) x = A sin ωt + B cos ωt
(ii) x = A sin ωt+ B cos 2ωt
(iii) x = A eiωt
(iv) x = A ln ωt

1. Show that the projection of uniform circular motion on a diameter is SHM.

2. Discuss how ripples are formed in still water.