Question

A body of mass \( 5 \, \text{m} \) initially at rest explodes into 3 fragments with mass ratio 3:1:1. Two of the fragments each of mass \( m \) are found to move with a speed of \( 60 \, \text{m/s} \) in mutually perpendicular directions. The velocity of the third fragment is

• A. \( 10 \sqrt{5} \, \text{m/s} \)
• B. \( 20 \sqrt{5} \, \text{m/s} \)
• C. \( 60 \, \text{m/s} \)
• D. \( 60 \, \text{m/s} \)

Hint:

In an explosion, the total momentum of the system is conserved, and the velocity of each fragment can be found by balancing the momenta.

Answer 1

The Correct Option is B

Step 1: Conservation of momentum.
The law of conservation of momentum states that the total momentum before and after the explosion remains constant. By solving for the momentum of the third fragment, we find its velocity to be \( 20 \sqrt{5} \, \text{m/s} \).

Step 2: Conclusion.
The velocity of the third fragment is \( 20 \sqrt{5} \, \text{m/s} \), which corresponds to option (2).