A solid cylinder is rolling down the inclined plane without slipping. Which of the following isare 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~ reduced

Answer

C, D

Explanation

Friction acts up the plane hence it hinders translation. But torque of friction produces rotation. So we can understand that option (c) is correct. We can write the following equations:
`mg sin theta- f =ma" "...(i)`
`fr=((1)/(2) mr^(2))((a)/(r)) rArr f=(1)/(2) ma " ".....(ii)`
On solving the above two equations we get friction:
`f=(1)/(3) mg sin theta`.hence magnitude of friction reduces when `theta` is reduced. So option (d) is also correct.