Q 11-05-014NEETJEE MainEAMCET 2014 (Engineering)Top questionMedium
A cannon shell fired breaks into two equal parts at its highest point. One part retraces the path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$. The relation between $E_1$ and $E_2$ is
Answer: (C) $E_2 = 9E_1$
At the highest point the shell (mass $2m$) moves horizontally with speed $v$. The part that retraces the path must move with velocity $-v$.
Momentum conservation: $2mv = m(-v) + mv_2 \Rightarrow v_2 = 3v$.
$$\frac{E_2}{E_1} = \frac{\frac{1}{2}m(3v)^2}{\frac{1}{2}mv^2} = 9 \;\Rightarrow\; E_2 = 9E_1$$
Solution by Sreeraj P, M.Sc Physics