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# A ball of mass 'm' moving at a spped 'v' makes a head-on collision with an identical ball at rest . The kinetic energy of the balls after the collision is three fourths of the original. Find the coefficient of restitution.

pratham ashish
9 Points
11 years ago
Hi, just considr initial vel. of I ball = u final vel. of I ball = v1 final vel. of II ball =v2 & coeff. of restitution = e now, e = vel. of separaion / vel. of approach e = v2 -v1 / u => v2-v1 = eu ....(1) momentum conservation => mu = mv1 +mv2 => u = v1 + v2 ...(2) energy eqn 3/4((mu^2)/2)= 1/2*m (v1^2 + v2^2) => 3/4*(u^2) = (v1^2 + v2^2) 2*(v1^2 + v2^2)=(v1 + v2)^2 + (v2 -v1)^2 = u^2 + (eu)^2 {FROM 1& 2 } => 3/2 (u^2) = u^2 + (eu)^2 => 1/2 (u^2) = (eu)^2 => e = root(1/2)
h v
33 Points
10 years ago