Types of collision

Question

A moving block having mass *m*, collides with another stationary block having mass *4 m*. The lighter block comes to rest after collision. When the initial velocity of the lighter block is *v*, then the value of coefficient of restitution *(e)* will be

Moderate

Solution

Let final velocity of the block of mass $4m={v}^{\text{'}}$

Initial velocity of block of mass *4 m=0*

Final velocity of block of mass *m=0*

According to law of conservation of linear momentum,

$\begin{array}{l}mv+4m\times 0=4m{v}^{\text{'}}+0\\ {v}^{\text{'}}=\frac{v}{4}\end{array}$

Coefficient of restitution,

$e=\frac{\text{Relative velocity of separation}}{\text{Relative velocity of approach}}=\frac{v/4}{v}$

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