A ring and a disc have the same mass and roll without slipping at the same linear velocity v. If the total kinetic energy of the ring is 8 J, then the total kinetic energy of the disc will be:

1. 8 J

2. 6 J

3. 16 J

4. 4 J

A solid homogenous sphere is moving on a rough horizontal surface, partially rolling and partially sliding. During this motion of this sphere:

1. The total kinetic energy is conserved.

2. The angular momentum of the sphere about the point of contact is conserved

3. Only the rotational kinetic energy about the centre of mass is conserved

4. Angular momentum about the centre of mass is conserved

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. There is no slipping anywhere. The length of the string that passed through the hand of the man while the cylinder reaches his hands is-[Assume radius of the cylinder is negligible compared to length 'l' of string]
       

A uniform sphere of mass m and radius r rolls without slipping down an inclined plane,  inclined at an angle of 45° to the horizontal. The minimum value of the coefficient of friction between the sphere and the inclined plane will be:

1. 1/6

2. 2/7

3. 1/5

4. 1/7

A disc hangs from an ideal string wrapped around it. If it is allowed to fall, the acceleration of the disc will be:

A block of mass m slides down on a smooth inclined plane and reaches the bottom with speed v. If the same mass is in the form of a ring which rolls down on an identical inclined plane, where friction is sufficient for pure rolling, the speed of the ring at the bottom will be:

1. $v$

2. $v\sqrt{2}$

3. $\frac{v}{\sqrt{2}}$

4. $v\sqrt{\frac{2}{5}}$

A hollow sphere of mass m is rolling with a speed v on a smooth horizontal surface and strikes a massless spring of force constant k attached to a massless smooth platform. The maximum compression of the spring will be:
            
1. $\sqrt{\frac{m}{k}}v$

2. $\sqrt{\frac{2m}{3k}}v$

3. $\sqrt{\frac{m}{5k}}v$

4. $\sqrt{\frac{5m}{3k}}v$

A solid cylinder of mass \(20\) kg rotates about its axis with angular speed \(100\) rad s^-1. The radius of the cylinder is \(0.25\) m. The kinetic energy associated with the rotation of the cylinder is:
1. \(3000\) J
2. \(3125\) J
3. \(2528\) J
4. \(2100\) J

A hoop of radius \(2\) m weighs \(100\) kg. It rolls along a horizontal floor so that its center of mass has a speed of \(20\) cm/s. How much work has to be done to stop it?
1. \(10\) J
2. \(9\) J
3. \(4\) J
4. \(6\) J

A solid cylinder rolls up an inclined plane of the angle of inclination 30°. At the bottom of the inclined plane, the centre of mass of the cylinder has a speed of 5 m/s. How far will the cylinder go up the plane?

1. 4.9 m
2. 1.3 m
3. 4.7 m
4. 3.8 m