Question

A ball of mas m moving t a speed v makes a head on collisiobn with a identicalbl at rest. The kinetic energy of the blls after the collision is three fourths of the original. Find the coefficient of retitutioin.

Answer 1

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`