1) The moment of inertia of a ring about a tangent to the circle of the ring is

2) The angular acceleration assuming it to be uniform is

3) How many revolutions does the engine make in 16 s.

4) What is the angular acceleration of the wheel?

5) The kinetic energy of the wheel, when 2 m of the cord has been pulled is

6) Three bodies, a ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. What is the velocity of the body that reaches down with the maximum velocity

7) The moment of inertia of a solid sphere about a tangent to the sphere, given the mass of the sphere is M and its radius is R, is

8) The moment of inertia of a disc of mass M and radius R about an axis normal to the disc and passing through a point on its edge is

9) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he holds his hands back and thereby reduces moment of inertia of the system

10) From a uniform disc of radius R, a circular hole of R/2 is cut out. The centre of the hole is R/2 from the centre of the original disc. The centre of gravity of the resulting body is at d from the centre of original disc opposite to the centre of cut portion d equals

11) A meter stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put on top of the other at the 12 cm mark, the stick is found to be balanced at 45 cm. The mass of the meter stick is

12) A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?

13) How far does the cylinder go up the plane?

14) How long does the cylinder take to return to the bottom?

15) A ring of mass 10 kg and diameter 0.4 m is rotated about its axis. If it makes 2100 revolutions per minute, then its angular momentum will be

16) For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of body?

17) Radius of gyration of a body about an axis at a distance of 6 cm from its centre of mass is 10 cm. The radius of gyration about a parallel axis through its centre of mass is

18) Without weighing, how will you distinguish between the two identical balls of same material, but one being solid and the other one being hollow?

19) A nearly mass less rod is pivoted at one end so that it can swing freely as a pendulum. Two masses 2 m and m are attached to it at distances b and 3 b respectively from the pivot. The rod is held horizontal and then released. The angular acceleration of the rod at the instant it is released is

20) A body rolls down an inclined plane. If its kinetic energy of rotational motion is 40% of its kinetic energy of translation then the body is

21) A paticle performs uniform circular motion with an angular momentum L. If the frequency of particle's motion is doubled and its kinetic energy is halved, then the angular momentum becomes

22) The radius of gyration of a circular plate of radius R, about an axis perpendicular to its plane and bisecting a radius is

23) Four particles, each of mass m, are placed symmetrically on the rim of a disc of mass M and radius R. The moment of inertia of this system about an axis passing through one of the particles and perpendicular to the plane of the disc is

24) Frictional force on the cylinder is

25) Acceleration of the cylinder is

26) Angular acceleration of the cylinder is

27) If the Earth shrinks to half the present radius, without any change in mass, then the duration of day and night becomes

28) Which of the following has the highest moment of inertia when each of them has the same mass and the same radius?

29) A uniform plane sheet of metal in the form of a triangle ABC has BC > A B > AC. Its moment of inertia will be smallest

30) A closed tube, partly filled with a liquid and set horizontal, is rotated about a vertical axis passing through its centre. In the process, the moment of inertia of the system about its axis would

31) A solid sphere, a spherical shell, a disc and a ring of the same radius are allowed to roll down an inclined plane simultaneously from the same height without slipping. Of these, the one which reaches the bottom first is

32) The ratio of the time taken by a uniform solid sphere and a disc of the same mass and diameter to roll down from rest the same distance on an inclined plane is

33) If the Earth is treated as a sphere of radius R and mass M, its angular momentum about the axis of its diurnal rotation with period T is

34) A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by 1%. The angular speed will approximately

35) A wheel of radius r and mass m stands in front of a step of height h. The least horizontal force which should be applied to the axle of the wheel to allow it to raise on the step is

36) A recording disc rotates steadily at 45 rev/min on a table. When a small mass of 0.02 kg is dropped gently on the disc at a distance of 0.04 m from its axis and sticks to the disc, the rate of revolution falls to 36 rev/min. The moment of inertia of the disc about its centre is

37) Statement 1 : Angular velocity is characteristic of a rigid body as a whole. Statement 2 : Angular velocity may be different for different particles of rigid body about axis of rotation.

38) Acceleration of plank is

39) Find coefficient of friction just needed to have sphere rolling on plank

40) Tension in string is