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NEETPhysicsCenter of Mass, Momentum and Collision

A moving particle of mass m collides head-on and elastically with a stationary particle of mass M (where M > m ). If the moving particle transfers 64 % of its initial kinetic energy to the stationary particle, the ratio M m is

Options

  1. A4
  2. B2
  3. C3
  4. D8

Correct answer

A. 4

Step-by-step solution

Let the initial velocity of the moving particle be u . For a perfectly elastic head-on collision with a stationary target, the fraction of kinetic energy transferred from the projectile to the target is given by: f = 4mM (m + M)^2 Given that 64 % of the initial kinetic energy is transferred: 4mM (m + M)^2 = 64 100 = 16 25 Dividing numerator and denominator by m^2 and letting the ratio M m = x : 4x (1 + x)^2 = 16 25 x 1 + 2x + x^2 = 4 25 Cross-multiplying gives: 25x = 4 + 8x + 4x^2 4x^2 - 17x + 4 = 0 Solving this qu

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