Question

Two small balls of masses ${}^{\prime }{m}^{\prime }$ and ${}^{\prime }2m^{\prime }$ are placed in a fixed smooth horizontal circular hollow tube of mean radius ${}^{\prime }{r}^{\prime }$ as shown. The ball of mass ${}^{\prime }{m}^{\prime }$ is moving with speed ${}^{\prime }{u}^{\prime }$ and the ball of mass ${}^{\prime }2m^{\prime }$ is stationary. After their first collision, the time elapsed for next collision is: (coefficient of restitution $e$ = $\frac{1}{2}$)

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$mu$ = $2m{V}_2-m{V}_1$ (from conservation of momentum)

$u$ = $2V_2-V_1$

$\frac{1}{2}$ = $\frac{V_2+V_1}{u}\Rightarrow 2V_2+2V_1$ = $u$[$\because e$ = $\frac{velocityofseparation}{velocityofapproach}$]

Solving, $V_1$ = 0, $V_2$ = $\frac{u}{2}$, $t$ = $\frac{2\pi r}{\frac{u}{2}}$ = $\frac{4\pi r}{u}$