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 transferrede to B initial energy of B=zero
Final velocity of
`V_(B)=((M_(2)-M_(1))/(M_(1)+M_(2)))u_(2)+(2M_(1)u_(1))/(M_(1)+M_(2))`
`M_(1)=4M" "u_(1)=u`
`M_(2)=2M" "u_(2)=0`
`V_(B)=(2(4M)u)/(6M)=(4)/(3)u`
`((1)/(2)M_(2)V_(B)^(2))/((1)/(2)M_(1)u_(1)^(2))=((1)/(2)2M((4)/(3))^(2)u^(2))/((1)/(2)4Mu^(2))`
Fraction of energy lost `=(8)/(9)`