PhysicsBody A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost of the colliding body A is :

Body A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost of the colliding body A is :

A
$\frac{4}{9}$
B
$\frac{5}{9}$
C
$\frac{1}{9}$
D
$\frac{8}{9}$

Solution:

Fractional loss of KE colliding body
$\begin{array}{l} \frac{ΔKE}{KE} = \frac{4 (m_{1} m_{2})}{{(m_{1} + m_{2})}^{2}} = \frac{4 (4 m) 2 m}{(4 m + 2 m)^{2}} \\ = \frac{32 m^{2}}{36 m^{2}} = \frac{8}{9} \end{array}$

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