Question

The first ball of mass $m$ moving with velocity $u$ collides head on with the second ball of mass $m$ at rest. If the coefficient of restitution is $e$, then the ratio of the velocity of the first and the seconds ball after the collision is

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

Answer 1

The correct option is A $\frac{1-e}{1+e}$

As the collision is head-on,
$mu+0=m{v}_1+m{v}_2$ or $u=v_1+v_2$ .........(i)
Further, coefficient of restitution is
$e=\frac{v_2-v_1}{u_1-u_2}=\frac{v_2-v_1}{u}$ $(\therefore u_2=0)$
or $eu=v_2-v_1$ ........(ii)
Adding Eqs. (i) and (ii), we get
$v_1=\frac{u(1-e)}{2},v_2=\frac{u(e+1)}{2}$ ..........(iii)
Now, $\frac{v_1}{v_2}=\frac{1-e}{1+e}$ ........(iv)