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Question

A hollow cylinder, a spherical shell, a solid cylinder and a solid sphere are allowed to roll on an inclined rough surface of coefficient of friction μ and inclination θ. The correct statements are

A
if cylindrical shell can roll on inclined plan, all other objects will also roll
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B
if all the objects are rolling and have same mass, the K.E. of all the objects will be same at the bottom of inclined plane
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C
work done by the frictional force will be zero, if objects are rolling
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D
frictional force will be equal for all the objects, if having same mass
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Solution

The correct options are
A if cylindrical shell can roll on inclined plan, all other objects will also roll
B if all the objects are rolling and have same mass, the K.E. of all the objects will be same at the bottom of inclined plane
C work done by the frictional force will be zero, if objects are rolling
Cylindrical shell has the highest moment of inertia among the four objects given. Thus A is right. Thus if it can roll then other bodies with lesser moment of inertia can also roll. Change in potential energy is same and no frictional lose in case of pure rolling then applying energy conservation we can see that K.E . will be same at bottom . Thus B is right. Also as it is the case of pure rolling, i.e velocity at the bottom is zero i.e there is no movement at the instantaneous center implying that the work done is zero. Thus option C is right.

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