Question 91 of 130

A body of mass $1kg$ collides head on elastically with a stationary body of mass $3kg$. After collision, the smaller body reverses its direction of motion and moves with a speed of $2m{s}^{-1}$. The initial speed of the smaller body before collision is ______ $m{s}^{-1}$.

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Answer: 4

Let ${u}_{1}$ be the initial speed of the smaller body before collision.
Let $v$ be the final speed of the bigger body after collision.
Applying conservation of linear momentum,
$1\times {u}_{1}+0=-2+3v \Rightarrow {u}_{1}=-2+3v...\left(1\right)$
We know, coefficient of restitution for elastic perfectly collision is $1$.
$\Rightarrow 1=\dfrac{v+2}{{u}_{1}} \Rightarrow v+2={u}_{1}...\left(2\right)$
Equating $\left(1\right)and\left(2\right)$, we have
${u}_{1}=4m{s}^{-1}$.