Question

A sphere of mass m moving with velocity u h its another stationary sphere of same mass. If e is the coefficient of restitution, what is the ratio of velocities of two spheres after the collision?

• A. $1:e$
• B. $\frac{1-e}{1+e}$
• C. $\frac{1+e}{1-e}$
• D. $1:e^2$

Answer 1

The correct option is B $\frac{1-e}{1+e}$

By definition of the coefficient of restitution

$e=\frac{v_2-v_1}{u_1-u_2}=\frac{v_2-v_1}{u=0}$

i.e

And by conservation of momentum

$mu-m{v}_1+m{v}_2$

or

$v_2+v_1=u$

Solving Equations (1) and (2) for $v_1$ and $v_2$ we get

$v_1=u(1-e)2$ and $v_2=u(1+e)2$

So,

$\frac{v_1}{v_2}=\left[\frac{1-e}{1+e}\right]$