Question

A sphere of mass $m$ moving with constant velocity $u$ , collides with another stationary sphere of same mass. If $e$ is the coefficient of restitution, the ratio of the final velocities of the first and second spheres is

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

Answer 1

Answer: (B)

Let $v_1,v_2$ be the final velocities of the two spheres.
Applying the law of conservation of linear momentum
$mu=m\left(v_1+v_2\right)$
or $v_1+v_2=u\dots$ (i)
Again the coefficient of restitution is given by
$e=\frac{v_2-v_1}{u}$
or $v_1+v_2=u\dots$ (ii)
Solving Eqs. (i) and (ii), we get
$v_1=\frac{u}{2}(1-e),v_2=\frac{u}{2}(1+e)$
Therefore, $\frac{v_1}{v_2}=\left(\frac{1-e}{1+e}\right)$