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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

  1. A3 : 4
  2. B9 : 16
  3. C16 : 9
  4. 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

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