Question 95 of 130

Three objects $A,B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of $A,B$ and $C$ are $m,2m$ and $2m$ respectively. $A$ moves towards $B$ with a speed of $9m{s}^{-1}$ and makes an elastic collision with it. Thereafter $B$ makes a completely inelastic collision with $C.$ All motions occur along the same straight line. The final speed of $C$ is :

A$6m{s}^{-1}$B$9m{s}^{-1}$C$4m{s}^{-1}$D$3m{s}^{-1}$

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Answer: (D) $3m{s}^{-1}$

Collision between $A$ and $B$

$m\times 9=m{v}_{1}+2m{v}_{2}$ (from momentum conservation)
$e=1=\dfrac{{v}_{2}-{v}_{1}}{9}$
$\Rightarrow {v}_{2}=6m{\sec }^{-1},{v}_{1}=-3m{\sec }^{-1}$
Collision between $B$ and $C$

$2m\times 6=4mv$ (from momentum conservation)
$v=3m{s}^{-1}$