Two bodies $A$ and $B$ of same mass undergo completely inelastic one-dimensional collision. The body

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Two bodies $A$ and $B$ of same mass undergo completely inelastic one-dimensional collision. The body $A$ moves with velocity $v_{1}$ while body $B$ is at rest before collision. The velocity of the system after collision is $v_{2}$. The ratio $v_{1}:v_{2}$ is

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Sol. [Key Concept: Completely inelastic collision — momentum conservation] Before collision $\Rightarrow (A) ightarrow v_{1}\ \underset{	ext{~}	ext{rest}	ext{~}}{(B)}$It undergoes completely inelastic collisionUsing conservation of linear momentumInitial momentum = Final momentum$$\begin{matrix} & \ \Rightarrow mv_{1} = mv_{2} + mv_{2} \ & \ \Rightarrow mv_{1} = 2mv_{2} \ & \ \Rightarrow \frac{v_{1}}{v_{2}} = \frac{2}{1} \end{matrix}$$

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