Question

A sphere of mass ${}^{\prime }{m}^{\prime }$ moving with velocity ${}^{\prime }{v}^{\prime }$ collides head-on on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is ($e$ is coefficient of restitution and collision is inelastic)

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

Answer 1

Answer: (C)

$\frac{e+1}{2}$

Let final velocities be $v_1$ and $v_2$ .

Now,coefficient of restitution,$e=\frac{v_2-v_1}{u}$

$v_2-v_1=eu$ $\left(i\right)$

And applying conservation of linear momentum:-

$mu=m{v}_1+m{v}_2$

$⟹v_2+v_1=u$ $\left(ii\right)$

Now, $\left(i\right)+\left(ii\right)$:-

$2v_2=u(1+e)$

$⟹\frac{v_2}{u}=\frac{1+e}{2}$

Hence, answer is option-(C).