A body of mass m moving with velocity v collides head on with another body of mass 2m which is initially at rest. The ratio of K.E of colliding body before and after collision will be

Explanation

Mas of 1st ball =m
and speed =v
Mass of 2nd ball =m
Let fiN/Al velocities of 1st and 2nd ball are `v_1 and v_2` respectively
Using law of conservation of momentum
`m(v_1+v_2)=mv`……i
`rarr v_1+v_2=v`…………ii
`also v_1-v_2=ev`
Given that fiN/Al K.E.`=3/4 initial K.E.
`rarr 1/2 mv_1^2+1/2mv_2^2=3/4xx1/2mv^2`
`rarr v_1^2+v_2^2=3/4v^2`
`rarr v_1^2+v_2^2=3/4v^2`
`rarr ((v_1+v_2)^2+(v_1-v_2)^2)/2=3/4v^2`
`rarr ((1+e^2)v^2)/2=3/4v^2`
rarr 1+e^2=(3/2)`
`rarr e^2=1/2`
`-e=1/sqrt2`