First slide

Types of collision

Question

A body of mass 4m is lying in .xy-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speeds v. The total kinetic energy generated due to explosion is

Moderate

A

mv²
B

(3 / 2) mv²
C

2 mv²
D

4 mv²

Solution

$\sqrt{2} (mv)$ = Resultant momentum of two small masses
$\sqrt{2} (mv) = (2 m) \times v' \Rightarrow v' = \frac{v}{\sqrt{2}}$
So, total kinetic energy generated by the explosion
$= \frac{1}{2} m v^{2} + \frac{1}{2} m v^{2} + \frac{1}{2} (2 m) v'^{2}$
$= m v^{2} + m \times {(\frac{v}{\sqrt{2}})}^{2} = m v^{2} + \frac{m v^{2}}{2} = \frac{3}{2} m v^{2}$

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