Question

A particle of mass 5 m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular direction with speed v each. the energy released during the process is :

• A. $\frac{3}{5}mv^{2}$
• B. $\frac{5}{3}mv^{2}$
• C. $\frac{3}{2}mv^{2}$
• D. $\frac{4}{3}mv^{2}$

Answer 1

The Correct Option is D

$3m\vec{v} + mv\hat{i} + mv\hat{j} = 0$
$\Rightarrow \vec{v} = -\frac{v}{3} \hat{i} - \frac{v}{3} \hat{j}$
$|\vec{v}| = \sqrt{2} \frac{v}{3}$
Energy released
$= \frac{1}{2} mv^2 + \frac{1}{2} mv^2 + \frac{1}{2} (3m) (\frac{2v^2}{9}) $
$=\frac{4}{3} mv^2$