First slide

Traslation Motion, Centre of mass as representative point

Question

A stationary body explodes into four identical fragments such that three of them flyoff mutually perpendicular to each other, each with same K.E., $E_{0}$ . The energy released in the explosion is

Moderate

A

$6 E_{0}$
B

$\frac{4 E_{0}}{3}$
C

$4 E_{0}$
D

$8 E_{0}$

Solution

By law of conservation of momentum,
$\begin{array}{l} v^{''} = - [{v^{'}}_{} \hat{i} + {v^{'}}_{} \hat{j} + v^{'} \hat{k}] \\ {(v^{''})}^{2} = 3 [{v^{'}}^{2}] \\ E_{0} = \frac{1}{2} m {v^{'}}^{2} \\ T o t a l E = 3 [\frac{1}{2} m {v^{'}}^{2}] + \frac{1}{2} m {v^{''}}^{2} \\ = 3 [E_{0}] + 3 E_{0} \\ = 6 E_{0} \end{array}$

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