Question

A sphere of mass $m$ moving with a constant velocity $u$ hits another stationary sphere of the same mass. If $e$ is the coefficient of restitution, then ratio of velocities of the two spheres after collision will be-

• A. $\left(\frac{1-e}{1+e}\right)$
• B. $\left(\frac{2+e}{1-e}\right)$
• C. $\left(\frac{e+1}{e-1}\right)$
• D. $\left(\frac{e-1}{e+1}\right)$

Answer 1

Answer: (A)

as $e=\frac{v_2-v_1}{u_1-u_2}=\frac{v_2-u}{u-0}$
$\Rightarrow v_2-v_1=eu$
from momentum conservation mu
$=m{v}_1+m{v}_2$
$\Rightarrow v_2+v_1=u$
solving equation (i) $\&$ (ii)
$v_1=\frac{u(1-e)}{2}\&v_2=\frac{u(1+e)}{2}$
so $\frac{v_1}{v_2}=\frac{1-e}{1+e}$