Question

As shown in figure, a uniform disc of mass $m$ is rolling without slipping with an angular velocity $\omega$. The portion $AB$ is rough and $BC$ is smooth. If the disc crosses point $B$, the motion of the disc will be:

• A. translational motion only
• B. pure rolling motion
• C. rotational motion only
• D. none of these

Answer 1

The correct option is B pure rolling motion

In case of pure rolling, velocities of contact points have to be equal.
i.e $V_P=V_Q$
$\&V=\omega R$ holds always

Since disc is already in a state of pure rolling, $V=\omega R$ is maintained. Hence friction won't act on the disc during its journey through the rough portion $AB$.
$\therefore$ Disc will continue pure rolling motion while it travels through smooth portion $BC$.