Reference no: EM132439929

Questions -

Part A -

1. A thin circular ring of mass M and radius r is rotating about its axis with an angular speed ω. Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become

(a) ωM/(M+m)

(b) ωM/(M+2m)

(c) ω(M-2m)/(M+2m)

(d) ω(M+2m)/M

2. A person sitting firmly over a rotating stool has his arms stretched. If he folds his arms, his angular momentum about the axis of rotation

(a) increases

(b) decreases

(c) remains unchanged

(d) doubles.

3. The centre of a wheel rolling on a plane surface moves with a speed v₀. A particle on the rim of the wheel at the same level as the centre will be moving at speed

(a) zero

(b) v₀

(c) √2v₀

(d) 2v₀

4. A wheel of radius 20 cm is pushed to move it on a rough horizontal surface. It is found to move through a distance of 60 cm on the road during the time it completes one revolution about the centre. Assume that the linear and the angular accelerations are uniform. The frictional force acting on the wheel by the surface is

(a) Along the velocity of the wheel

(b) Opposite to the velocity of the wheel

(c) Perpendicular to the velocity of the wheel

(d) Zero.

5. The angular velocity of the engine (and hence of the wheel) of a scooter is proportional to the petrol input per second. The scooter is moving on a frictionless road with uniform velocity. If the petrol input is increased by 10%, the linear velocity of the scooter is increased by

(a) 50%

(b) 10%

(c) 20%

(d) 0%.

6. A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of a smooth incline and released. Least time will be taken in reaching the bottom by

(a) the solid sphere

(b) the hollow sphere

(c) the disc

(d) all will take same time

7. A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. Least time will be taken in reaching the bottom by

(a) the solid sphere

(b) the hollow sphere

(c) the disc

(d) all will take same time.

8. In the previous question, the smallest kinetic energy at the bottom of the incline will be achieved by

(a) the solid sphere

(b) the hollow sphere

(c) the disc

(d) all will achieve same kinetic energy

9. A string of negligible thickness is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance l from the cylinder holds one end of the string and pulls the cylinder towards him (figure 10-Q4). There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands is

(a) l

(b) 2l

(c) 3l

(d) 4l.

Part B -

1. The axis of rotation of a purely rotating body

(a) must pass through the centre of mass

(b) may pass through the centre of mass

(c) must pass through a particle of the body

(d) may pass through a particle of the body.

2. Consider the following two equations

(A) L = Iω

(B) dL/dt = Γ

In noninertial frames

(a) both A and B are true

(b) A is true but B is false

(c) B is true but A is false

(d) both A and B are false.

3. A particle moves on a straight line with a uniform velocity. Its angular momentum

(a) is always zero

(b) is zero about a point on the straight line

(c) is not zero about a point away from the straight line

(d) about any given point remains constant.

4. If there is no external force acting on a non-rigid body, which of the following quantities must remain constant?

(a) angular momentum

(b) linear momentum

(c) kinetic energy

(d) moment of inertia.

Q5. Let I_A and I_B be moments of inertia of a body about two axes A and B respectively. The axis A passes through the centre of mass of the body but B does not.

(a) I_A < I_B

(b) If I_A < I_B, the axes are parallel

(c) If the axes are parallel, I_A < I_B

(d) If the axes are not parallel, I_A ≥ I_B.