Question

Two identical small spheres A and B lie on a smooth horizontal circular groove at opposite ends of diameter. A is projected along the groove and it hits B at time t. If e is the coefficient of restitution, then the second impact will occur after the time.

• A. $\frac{2t}{e}$
• B. $\frac{t}{e}$
• C. $\frac{\pi t}{e}$
• D. $\frac{2\pi t}{e}$

Answer 1

The correct option is A $\frac{2t}{e}$

Let ‘t’ be the time taken before first collision, $t=\frac{\pi r}{u}$
Let t’ be the time after which next collision takes place t = $t^{\prime }=\frac{\text{Relative displacement}}{\text{Relative velocity}}$

Relative velocity is $V_{rel}=\{\left(\frac{1+e}{2}\right)u-\left(\frac{1-e}{2}\right)u\}$ $V_{rel}=eu$ $\therefore t^{\prime }=\frac{2\pi r}{eu}=\frac{2t}{e}$