Question

A solid uniform sphere of mass 5 kg and radius 0.1 m rolls down an inclined plane without slipping. if the sphere's center of mass moves through a vertical distance of 1.5 m , what is the rotational work done on the sphere by the static-friction force?

Answer 1

Since sphere is performing pure rolling motion

So here the contact point of sphere with respect to inclined plane is always at rest.

This contact point will not move at any instant and and hence sphere will perform pure rolling.

So here we can say that sphere will have some friction force at the contact point but there is no displacement of that point.

So the work done by this static friction will always ZERO.

$W_{friction} = F.d$

$W_{friction} = 0$

So there is no work done by friction on the sphere while it is in pure rolling.