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 colliding body `A` is :

Options

A. `5/9`
B. `1/9`
C. `8/9`
D. `4/9`

Answer

C

Explanation

Energy transferred to B initial energy of B = zero Final velocity of
`V_B = ((M_2-M_1)/(M_1+M_2)) u_2 +(2M_1u_1)/(M_1+M_2)`
`M_1 = 4m u_1 =u`
`M+2 = 2m u_2 =0`
`V_B = (2(4m)u)/(6m) =4/3u`
`implies (E_("final"))/(E_("initial"))=(1/2M_2V_B^2)/(1/2M_1u_1^2)=(1/(2)2m(4/3)^2u^2)/(1/(2) 4"mu"^2)`
Fraction of energy lost `=8/9`