First slide

The steps in collision

Question

A particle of mass m collides with another stationary particle of mass M. If the particle m stops just after collision, then the coefficient of restitution for collision is equal to

Easy

A

1
B

$\frac{m}{M}$
C

$\frac{M - m}{M + m}$
D

$\frac{m}{M + m}$

Solution

As, net horizontal force acting on the system is zero, hence momentum must remain conserved.
Hence, $m u + 0 = 0 + M v_{2}$
$\Rightarrow$ $v_{2} = \frac{m u}{M}$
Coefficient of restitution, $e = \frac{|(v_{2} - v_{1})|}{|(u_{2} - u_{1})|} = \frac{|v_{2} - 0|}{| 0 - u |}$
$= \frac{v_{2}}{u} = \frac{\frac{m u}{M}}{u} = \frac{m}{M}$

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