A circular disc of mass 2 kg and radius 10 cm rolls without slipping with a speed 2 m/s. The total kinetic energy of disc is

(1) 10 J

(2) 6 J

(3) 2 J

(4) 4 J

A horizontal disc rotating freely about a vertical axis through its centre makes 90 revolutions per minute. A small piece of wax of mass m falls vertically on the disc and sticks to it at a distance r from the axis. If the number of revolutions per minute reduce to 60 , then the moment of inertia of the disc is

(1) mr²

(2) $\frac{3}{2}m{r}^2$

(3) 2 mr²

(4) 3 mr²

The angular momentum of a particle performing uniform circular motion is L. If the kinetic energy of partical is doubled and frequency is halved, then angular momentum becomes

(1) $\frac{L}{2}$

(2) 2L

(3) $\frac{L}{4}$

(4) 4L

A uniform rod of mass m and length l is suspended by two strings at its ends as shown. When one of the strings is cut, the rod starts falling with an initial angular acceleration

(1) $\frac{g}{l}$

(2) $\frac{g}{2l}$

(3) $\frac{3g}{2l}$

(4) $\frac{3g}{4l}$

Two like parallel forces 20 N and 30 N act at the ends A and B of a rod 1.5 m long. The resultant of the forces will act at the point

(1) 90 cm from A

(2) 75 cm from B

(3) 20 cm from B

(4) 85 cm from A

A disc of mass m and radius r is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass m is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height h, is

(1) $\sqrt{2gh}$

(2) $\sqrt{\frac{2}{3}gh}$

(3) $2\sqrt{\frac{gh}{3}}$

(4) $\frac{1}{2}\sqrt{3gh}$

When a body is rolling without slipping on a rough horizontal surface, the work done by friction is

(1) Always zero

(2) May be zero

(3) Always positive

(4) Always negative

A solid cylinder of mass M and radius R rolls down an inclined plane of height h without slipping. The speed of its centre of mass when it reaches the bottom is

(1) $\sqrt{2gh}$

(2) $\sqrt{\frac{4}{3}gh}$

(3) $\sqrt{\frac{3}{4}gh}$

(4) $\sqrt{\frac{4g}{h}}$

A ball is travelling with uniform translatory motion. This means that:

1. It is at rest.

2. The path can be a straight line or circular and the ball travels with uniform speed.

3. All parts of the ball have the same velocity (magnitude and direction) and the velocity is constant.

4. The centre of the ball moves with constant velocity and the ball spins about its centre uniformly.

A metre scale is moving with uniform velocity. This implies:

1. The force acting on the scale is zero, but a torque about the centre of mass can act on the scale.

2. The force acting on the scale is zero and the torque acting about centre of mass of the scale is also zero.

3. The total force acting on it need not be zero but the torque on it is zero.

4. Neither the force nor the torque need to be zero.