Bob $B$ of mass $m$ at rest is hanging vertically from the ceiling via a massless string of length $10$ m, as shown in the figure. Point mass $A$ of mass $m$ travelling horizontally with speed $10\ \text{m s}^{-1}$ hits bob $B$ elastically. The bob $B$ rises $h$ meter after the collision. Taking the acceleration due to gravity $g = 10\ \text{m s}^{-2}$ and neglecting the size of the bob, the value of $h$ is :
Answer: (C) $5$
In a one-dimensional elastic collision between equal masses, the velocities are exchanged. So A stops and B moves off with $10\ \text{m s}^{-1}$.
Energy conservation for the bob:
$$h = \frac{v^2}{2g} = \frac{10^2}{2 \times 10} = 5\ \text{m}$$
Since $h = 5$ m is less than the string length ($10$ m), the string stays taut and the bob simply swings up to this height.
Solution by Sreeraj P, M.Sc Physics