Question

A cannon shell fired breaks into two equal parts at its highest point. One part retraces the path to the cannon with energy $E_1$ and kinetic energy of the second part is $E_2$. Relation between $E_1$ and $E_2$ is:

• A. $E_2=15E_1$
• B. $E_2=E_1$
• C. $E_2=4E_1$
• D. $E_2=9E_1$

Answer 1

The correct option is D $E_2=9E_1$

Applying conservation of meomntum:

$MV=\frac{-MV}{2}+\frac{M{V}^{\prime }}{2}$

$MV+\frac{MV}{2}=\frac{M{V}^{\prime }}{2}$

$\Rightarrow V^{\prime }=3V$

$\frac{K_1}{K_2}=\frac{\frac{1}{2}M{V}^2}{\frac{1}{2}M(3V{)}^2}=\frac{1}{9}$

$\frac{E_1}{E_2}=\frac{1}{9}\Rightarrow E_2=9E_1$