A sphere of mass' $m$ ' moving with velocity ' $v$ 'collides head-on another sphere of same mass which is at…

A sphere of mass' $m$ ' moving with velocity ' $v$ 'collides head-on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is ( $e$ is coefficient of restitution and collision is inelastic)
  1. $\frac{e-1}{2}$
  2. $\frac{e}{2}$
  3. $\frac{e+1}{2}$
  4. $e$

Solution

$\begin{aligned} & m V+0=m V_1+m V_2 \\ & V_1+V_2=V \ldots \ldots .(1) \\ & e=\frac{V_2-V_1}{u_1-u_2} \\ & e=\frac{V_2-V_1}{V-0} \\ & e V=V_2-V_1 \ldots \ldots .(2) \end{aligned}$ By solving these equations, $\begin{aligned} & e V+V=2 V_2 \\ & V_2=\frac{V(e+1)}{2} \\ & \frac{V_2}{V}=\frac{e+1}{2} \end{aligned}$

Asked in: MHT CET 2022 (08 Aug Shift 1)

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