Three objects A, B and C are kept in a straight line on a frictio… - Vidyadip

Question

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 ${m}, 2\, {m}$ and $2\, {m}$ respectively. $A$ moves towards ${B}$ with a speed of $9$ ${m} / {s}$ and makes an elastic collision with it. Thereafter $B$ makes a completely inelastic collision with $C.$ All motions occur along same straight line. The final speed of $C$ is $....\,{m} / {s}$

✓

Answer

After $1^{st}$ collision

$m v_{A}=m v_{A}^{\prime}+2 m v_{B}^{\prime}$

$-1=\frac{v_{B}^{\prime}-v_{A}^{\prime}}{0-v_{A}} \Rightarrow v_{B}^{\prime}=6 m / s$

After the $2^{nd}$ collision

$2 mv _{ B }^{\prime}=(2 m + m )_{ V _{ C }}$

$\Rightarrow v _{ C }=\frac{2}{3} v _{ B }^{\prime} \Rightarrow v _{ C }=4 m / s$

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