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A sphere of mass $m$ moving with velocity $v$ hits inelastically with another stationary sphere of same mass. The ratio of their final velocities will be (in terms of $e$ )
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Verified Answer
The correct answer is:
$\frac{v_1}{v_2}=\frac{1-e}{1+e}$
As coefficient of restitution, $e=\frac{v_2-v_1}{u_1-u_2}=\frac{v_2-v_1}{u-0}$
$\Rightarrow \quad v_2-v_1=e u$...(i)
By conservation of momentum,
Momentum before collision = Momentum after collision
$\begin{aligned} & m u=m v_1+m v_2 \\ & \Rightarrow \quad v_1+v_2=u \\ & \end{aligned}$...(ii)
On solving Eqs. (i) and (ii), we get
$\begin{aligned} & v_1=\frac{u}{2}(1-e) \text { and } v_2=\frac{u}{2}(1+e) \\ & \therefore \quad \frac{v_1}{v_2}=\frac{1-e}{1+e} \\ & \end{aligned}$
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