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 the ratio of the velocity of two spheres after collision will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let the final velocities of the two masses be $v_1$ and $v_2$ By definition,$e=\frac{v_2-v_1}{0-4}$
Conservation of linear momentum,$m\left(u\right)+0=m{v}_1+m{v}_2$
$\Rightarrow v_1+v_2=4$
$\therefore \frac{v_1+v_2}{v_2-v_1}=\frac{4}{-e4}$
$\frac{v_1+v_2}{v_1-v_2}=\frac{1}{e}$
$\therefore \frac{v_1}{v_2}=\frac{1+e}{1-e}$
$\frac{v_2}{v_1}=\frac{1-e}{1+e}$