Question

A sphere $A$ of mass $m$ moving with a velocity hits another stationary sphere $B$ of same mass. If the ratio of the velocities of the spheres after collision is $\frac{v_A}{v_B}=\frac{1-e}{1+e}$ where $e$ is the coefficient of restitution, what is the initial velocity of spheres $A$ with which it strikes

• A. $v_A-v_B$
• B. $v_B-v_A$
• C. $\frac{(v_A+v_B)}{2}$
• D. $v_A+v_B$

Answer 1

The correct option is D $v_A+v_B$

Given,

$\frac{v_A}{v_B}=\frac{1-e}{1+e}$

$\frac{v_A}{v_B}-1=\frac{1-e}{1+e}-1$

$v_B-v_A=\frac{2e}{1+e}\cdot v_B$

But

$e=\frac{v_B-v_A}{u}$

$ue=\frac{2e{v}_B}{(1+e)}$

$\Rightarrow u+eu=2v_B$

$u+(v_B-v_A)=2v_B\Rightarrow u=v_A+v_B$