Question

A disc of mass $m$ and radius $r$ is placed on a rough horizontal surface. A cue of mass $m$ hits the disc at a height $\frac{r}{2}$ from the axis passing through centre and parallel to the surface, as shown. The cue stops and falls down after the impact. The disc starts its motion as:

• A. Rolling with forward slipping
• B. Pure slipping
• C. Pure rolling
• D. Rolling with backward slipping

Answer 1

The correct option is C Pure rolling

According to question,
Linear momentum is conserved.
$mv=m{v}^{\prime }$ or $v=v^{\prime }$
Angular momentum about centre of disc,
$\therefore mv\frac{r}{2}=I\omega$
Therefore,
$mv\frac{r}{2}=\frac{m{r}^2}{2}.\omega$
$v=r\omega$
Hence, above condition is for pure rolling motion.

Final answer: (a)