Question

A sphere of mass m moving with a constant velocity hits another stationary sphere of the same mass. If e is the coefficient of restitution, then a ratio of the speed of the first sphere to the speed of the second sphere after head-on collision will be:

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

Answer 1

The correct option is A $\left(\frac{1-e}{1+e}\right)$

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

$eu=v_2-v_1$

For head on elastic collision: $u=v_1+v_2$

On solving we get:

$v_1=(1-e)\frac{u}{2},v_2=(1+e)\frac{u}{2}$
$\frac{v_1}{v_2}=\frac{1-e}{1+e}$