#### Important questions -chapter 5,6

11th Standard

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Physics

Use blue pen Only

Time : 01:30:00 Hrs
Total Marks : 115
Part A

15 x 1 = 15
1. A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force 30 N?

(a)

(b)

(c)

5 m S-2

(d)

25 m S-2

2. A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia,

(a)

Increases

(b)

decreases

(c)

remains constant

(d)

depends on direction of rotation.

3. A disc of the moment of inertia Ia is rotating in a horizontal plane about its symmetry axis with a constant angular speed $\omega$ Another disc initially at rest of moment of inertia Ib is dropped coaxially on to the rotating disc. Then, both the discs rotate with the same constant angular speed. The loss of kinetic energy due to friction in this process is,

(a)

$\frac { 1 }{ 2 } \frac { { I }_{ b }^{ 2 } }{ 2({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }$

(b)

$\frac { { I }_{ b }^{ 2 } }{ 2({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }$

(c)

$\frac { { ({ I }_{ b }-{ I }_{ a }) }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }$

(d)

$\frac { 1 }{ 2 } \frac { { { I }_{ b }{ I }_{ b } } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }$

4. The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle $\theta$ without slipping and slipping down the incline without rolling is,

(a)

5 : 7

(b)

2: 3

(c)

2: 5

(d)

7: 5

5. The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height his,

(a)

$\sqrt \frac{4}{3}gh$

(b)

$\sqrt \frac{10}{7}gh$

(c)

$\sqrt{2gh}$

(d)

$\sqrt \frac{1}{2}gh$

6. A body is rolling down an inclined plane. Its translational and rotational kinetic energies are equal. The body is a:

(a)

solid sphere

(b)

hollow sphere

(c)

solid cylinder

(d)

hollow cylinder

7. ABC is an equilateral triangle with O as its centre.$\overrightarrow{F_1},\overrightarrow{F_2}and \overrightarrow{F_3}$represent three forces acting along
the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of $\overrightarrow{F_3}$ is

(a)

F1 + F2

(b)

F1 - F2

(c)

${F_1+F_2\over 2}$

(d)

2(F1 + F2)

8. Sliding of the object occurs when

(a)

Vtrans<Vrot

(b)

Vtrans=Vrot

(c)

Vtrans>Vrot

(d)

Vtrans=0

9. Infinitesimal quantity means

(a)

collective particles

(b)

extremely small

(c)

nothing

(d)

extremely larger

10. Unit of moment of inertia

(a)

kgm

(b)

mkg-2

(c)

kgm2

(d)

kgm-1

11. The linear momentum and position vector of the planet is perpendicular to each other at

(a)

perihelion and aphelion

(b)

at all points

(c)

only at perihelion

(d)

no point

12. The work done by the Sun’s gravitational force on the Earth is

(a)

always zero

(b)

always positive

(c)

can be positive or negative

(d)

always negative

13. If the mass and radius of the Earth are both doubled, then the acceleration due to gravity g'

(a)

remains same

(b)

${g\over 2}$

(c)

2g

(d)

4g

14. The magnitude of the Sun’s gravitational field as experienced by Earth is

(a)

same over the year

(b)

decreases in the month of January and increases in the month of July

(c)

decreases in the month of July and increases in the month of January

(d)

increases during day time and decreases during night time

15. If a person moves from Chennai to Trichy, his weight

(a)

increases

(b)

decreases

(c)

remains same

(d)

increases and then decreases

16.

Part B

10 x 2 = 20
17. State the torque about an axis is independent of the origin.

18. Why centripetal force cannot do work?

19. Three blocks of uniform thickness and masses m, m and 2m are placed at three corners of a triangle having co-ordinates (2.5, 1.5) (3.5, 1.5) and (3, 3) respectively. Find the centre of mass of the system.

20. When an object be in mechanical equilibrium?

21. State the principle of moments of rotational equilibrium.

22. Can the couple acting on a rigid body produce translator motion?

23. Which component of linear momentum does not contribute to angular momentum?

24. If the Earth has no tilt, what happens to the seasons of the Earth?

25. Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. Calculate the speed of each particle

26. An object is thrown from Earth in such a way that it reaches a point at infinity with non-zero kinetic energy [K.E(r=$\infty$)= ${1\over 2}MV_{\infty}^2$], with what velocity should the object be thrown from Earth?

27.  Part C

10 x 3 = 30
28. Explain how the torque can be expressed as a vector product of two vectors, how is the direction and magnitude of torque is determined?

29. What is rolling motion?

30. The diameter of a solid disc is 0.5m and its mass is 16kg. What torque will increase Its angular velocity from zero to 120 rotations/minute in 8 seconds?

31. Calculate the moment of inertia of a cylinder of length 1.5m, radius 0.05m and density 8 X 103 kg m-3 about the axis of the cylinder.

32. A star of mass twice the solar mass and radius 106 km rotates about its axis with an angular speed of 10-6 rad s-1. What is the angular speed of the star when it collapses (due to inward gravitational force) to a radius of 104 km? Solar mass 1.99 x 1030 kg.

33. A car weighs 1800 kg. The distance between its front and back axles is 1·8 m. Its centre of gravity is 1·05 m behind the front axle. Determine the force exerted by the level ground on each front and back wheel.

34. Three mutually perpendicular beams AB, OC, GR are fixed to form a structure which is fixed to the ground firmly as shown in the Figure. One string is tied to the point C and its free end D is pulled with a force F. Find the magnitude and direction of the torque produced by the force,
(i) about the points D, C, 0 and B
(ii) about the axis CD, OC, AB and GR.

35. What is meant by superposition of gravitational field?

36. Define gravitational potential.

37. How will you prove that Earth itself is spinning?

38.  Part D

10 x 5 = 50
39. Obtain the relation between Torque and angular acceleration.

40. Write an expression for the kinetic energy of a body in pure rolling.

41. A uniform disc of mass 100g has a diameter of 10 cm, Calculate the total energy of the disc when rolling along a horizontal table with a velocity of 20 cms-1. (take the surface of table as reference).

42. Calculate the CG of plane lamina by pivoting method.

43. Derive an expression for center of mass for distributed point masses.

44. A disc of mass 500 g and radius 10 em can freely rotate about a fixed axis as shown in figure. light and inextensible string is wound several turns around it and 100 g body is suspended at its free end. Find the acceleration of this mass. [Given: The string makes the disc to rotate and does not slip over it. g = 10m s-2]

45. From a complete ring of mass M and radius R, a sector angle $\theta$ is removed. What is the moment of inertia of the incomplete ring about axis passing through the center of the ring and perpendicular to the plane of the ring?

46. Explain how Newton arrived at his law of gravitation from Kepler’s third law.

47. Explain the variation of g with altitude.

48. Explain in detail the Eratosthenes method of finding the radius of Earth.