First slide

Types of collision

Question

A ball of mass m moving with a speed u undergoes a head on collision with a ball of mass n m initially at rest. The fraction of incident energy transferred to heavier ball is

Moderate

A

$\frac{n}{1 + n}$
B

$\frac{n}{(1 + n)^{2}}$
C

$\frac{2 n}{(1 + n)^{2}}$
D

$\frac{4 n}{(1 + n)^{2}}$

Solution

. Fraction of energy transferred
$= 1 - {(\frac{v_{1}}{u_{1}})}^{2} = 1 - {(\frac{m - nm}{m + nm})}^{2} = 1 - \frac{(1 - n)^{2}}{(1 + n)^{2}} = \frac{4 n}{(1 + n)^{2}}$

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