A hollow cylinder, a spherical shell, a solid cylinder and a solid sphere are allowed to roll purely on an inclined rough surface of inclination . The CORRECT statement(s) is/are:

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If all the objects have same mass, the K.E. of the all the objects will be same at the bottom of inclined plane

Frictional force will be equal for all the rolling objects, if having same mass

If cylindrical shell can roll on inclined plane, all other objects will also roll.

Work done by the frictional force will be zero.

answer is B, C, D.

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Detailed Solution

For all four cases , initial gravitational potential energy is converted in KE.

Point of action of static frictional force is not moving .

$f = \frac{m g \sin θ}{1 + \frac{m R^{2}}{I}}$

No displacement of point of contact. So work done $= 0$

$μ > \frac{g \tan θ}{1 + \frac{m R^{2}}{I}}$

$F o r m a x i m u m I, μ_{r e q d} i s m a x .$

$I i s m a x i m u m f o r h o l l o w c y l i n d e r .$ is for hollow cylinder.

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