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 sphere 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: (A)

using momentum conservation
$v_1+v_2=u$

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

$\Rightarrow v_2-v_1=eu$

$\Rightarrow v_2=\frac{(1+e)}{2}u$

$\Rightarrow v_1=\frac{(1-e)}{2}u$

$v_1:v_2=\frac{1-e}{1+e}$