Question

Two equal spheres $A$ and $B$ lie on a smooth horizontal circular groove at opposite ends of a diameter. At time $t=0,A$ is projected along the groove and it first impinges on $B$ at time $t=T_1$ and again at time $t=T_2$. If e is the coefficient of restitution, the ratio $T_2/T_1$ is

• A. $\frac{2}{e}$
• B. $\frac{\left(2+e\right)}{2}$
• C. $\frac{2\left(e+1\right)}{e}$
• D. $\frac{\left(2+e\right)}{e}$

Answer 1

Answer: (D)

$T_1=\frac{\pi R}{u_1}(1)$

Time taken to collide $A$ and $B$ again:
$T_2-T_1=\frac{2\pi R}{v_2-v_1}$
$\Rightarrow T_2-T_1=\frac{2\pi R}{e{u}_1}(2)$
$(2)+(1)\Rightarrow \frac{T_2}{T_1}=\frac{2+e}{e}$