Question

A solid sphere is in pure rolling motion on an inclined surface having inclination $\theta$, $\theta$-

• A. frictional force acting on sphere is $f=\mu mg\cos \theta$
• B. $f$ is dissipative force
• C. friction will increase its angular velocity and decreases its linear velocity
• D. None of these

Answer 1

The correct option is C friction will increase its angular velocity and decreases its linear velocity

$\begin{array}{c}\text{* The frictional for u opposes the linear motion of}\\ \text{the body, therefore it reduces the linear}\\ \text{velocity of the body}\\ \text{* some frictional force will be applied which}\\ \text{is alwasys less than umgcos}\theta \text{because}\end{array}$

$\begin{array}{c}\text{the sphere is not sliding, and no energy dissipation}\\ \ast \text{The frictional foru supports the rotational motion}\\ \text{of the sphere and hence it increases its}\\ \text{angular velocity.}\\ \text{Hence, option (C) is correct.}\end{array}$