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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 ms$^{-1}$ hits bob B elastically. The bob B rises h meter after the collision. Taking the acceleration due to gravity g = 10 ms$^{-2}$ and neglecting the size of the bob, the value of h is:
Detailed Solution
The masses are equal and the collision is head-on and elastic, so the velocities interchange: B moves off with 10 m/s. By conservation of mechanical energy, $\frac{1}{2}mv^2=mgh \Rightarrow h=\frac{v^2}{2g}=\frac{100}{20}=5$ m.