A solid cylinder is rolling down the inclined plane without slipping. Which of the following is/are correct ?

Options

A. The friction force is dissipative
B. The friction force is necessarily changing
C. The friction force will aid rotation but hinder translation
D. The friction force is reduced, if `theta` is reduced

Answer

C, D

Explanation

Acceleration of centre of mass of cylinder is given by
`a_(cm)=(gsintheta)/(1+(I_(cm))/(MR^(2)))=(gsintheta)/(1+(MR^(2)//2)/(MR^(2)))=(2gsintheta)/(3)`
Since, `Mgsintheta-f=Ma_(cm)=M(2gsintheta)/(3)`
`therefore f=(Mgsintheta)/(3)`
Thus when `theta` is reduced, friction f will also decrease. Since point of application of frictional force is instantaneously at rest, the work done by friction will be zero, hence frictional force is not dissipative.

Further, as frictional force is static, its value can lie from 0 to `mumg cos theta` but not necessarily equal to `mumg cos theta`. Hence, the frictional force will provide torque for rotation but it will oppose translation.