Three objects $A$, $B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of $A$, $B$ and $C$ are $m$, $2m$ and $2m$ respectively. $A$ moves towards $B$ with a speed of $9\ \text{m s}^{-1}$ and makes an elastic collision with it. Thereafter $B$ makes a completely inelastic collision with $C$. All motions occur along the same straight line. The final speed of $C$ is:
Answer: (D) $3\ \text{m s}^{-1}$
Elastic collision of $A$ ($m$, $9$ m/s) with $B$ ($2m$, at rest):
$$v_B = \frac{2m_A}{m_A + m_B}u = \frac{2m}{3m}\times 9 = 6\ \text{m s}^{-1}$$
Perfectly inelastic collision of $B$ with $C$ (both $2m$): $2m(6) = 4m\,v \Rightarrow v = 3\ \text{m s}^{-1}$.
$C$ moves together with $B$ at $3\ \text{m s}^{-1}$.
Solution by Sreeraj P, M.Sc Physics