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NEET2019PhysicsCenter of Mass, Momentum and CollisionActual

Body A of mass 4 m moving with speed u collides with another body B of mass 2 m at rest. The collision is head on and elastic in nature. After the collision, the fraction of energy lost by the colliding body A is

Options

  1. A1 9
  2. B8 9
  3. C4 9
  4. D5 9

Correct answer

B. 8 9

Step-by-step solution

4 m u + 0 = 4 m v 1 + 2 m v 2 ⇒ 2 u = 2 v 1 + v 2   … ( A ) For elastic collision, e = 1 ⇒ u = v 2 - v 1   … ( B ) From A   and B , 4 u = 3 v 2 ⇒ v 2 = 4 3 u and v 1 = u 3 Fraction of energy lost by ( A ) , = 1 2 4 m u 2   -   1 2 4 m v 1 2 1 2 4 m u 2 = u 2   -   u 2 9 u 2 = 8 9

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