JEE Main202313 Apr 2023Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual
Two bodies are having kinetic energies in the ratio 16 : 9 . If they have same linear momentum, the ratio of their masses respectively is:
Options
- A3 : 4
- B9 : 16
- C16 : 9
- D4 : 3
Correct answer
B. 9 : 16
Step-by-step solution
The kinetic energy and the momentum of a moving object are related by K = p 2 2 m       . . . 1 Hence, the ratio of the kinetic energies of two objects having masses m and m ' can be calculated as follows: K K ' = p 2 2 m p 2 2 m ' = m ' m       . . . 2 Substitute the ratio of the kinetic energies into equation (2) and simplify to obtain the ratio of their masses. ⇒ 16 9 = m ' m ⇒ m : m ' = 9 : 16