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Physics Question on work, energy and power

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 by the colliding body A is :

A

49\frac{4}{9}

B

59\frac{5}{9}

C

19\frac{1}{9}

D

89\frac{8}{9}

Answer

89\frac{8}{9}

Explanation

Solution

Fractional loss of KE of ccolliding body
ΔKEKE=4(m1m2)(m1+m2)2\frac{\Delta KE}{KE} = \frac{4\left(m_{1}m_{2}\right)}{\left(m_{1} + m_{2}\right)^{2}}
=4(4m)2m(4m+2m)2= \frac{4\left(4m\right)2m}{\left(4m+2m\right)^{2}}
=32m236m2=89= \frac{32m^{2} }{36m^{2}} = \frac{8}{9}