Velocity of Exploded Fragment – Rankers Physics
Topic: Center of Mass , Momentum and Collision
Subtopic: Collision

Velocity of Exploded Fragment

A stationary body of mass m explodes into 3 parts with mass ratio of \(1 : 3 : 3\). The two fragments with equal mass move at right angles to each other with velocity of \(15\text{ ms}^{-1}\). The velocity of the third fragment is (in \(\text{ms}^{-1}\)):
\(15\sqrt{2}\)
5
\(20\sqrt{2}\)
\(45\sqrt{2}\)

Solution:

The ratio of masses is \(m' : 3m' : 3m'\). The combined momentum of the two perpendicular \(3m'\) masses is \(P = \sqrt{(3m' \times 15)^2 + (3m' \times 15)^2} = 45\sqrt{2} m'\). Conservation of momentum requires the third fragment \(m'\) to balance this: \(m' v_3 = 45\sqrt{2} m' ⇒ v_3 = 45\sqrt{2}\text{ ms}^{-1}\).

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