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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

Two particles of masses M and 2 M are moving with speeds of 10 m s - 1 and 5 m s - 1 , as shown in the figure. They collide at the origin and after that they move along the indicated directions with speeds v 1 and v 2 , respectively. The values of v 1 and v 2 are, nearly

Options

  1. A6.5 m s - 1 and 3.2 m s - 1
  2. B3.2 m s - 1 and 12.6 m s - 1
  3. C13.02 m s - 1 and 19 . 7 m s - 1
  4. D3.2 m s - 1 and 6.3 m s - 1

Correct answer

C. 13.02 m s - 1 and 19 . 7 m s - 1

Step-by-step solution

From conservation of linear momentum, Along x -axis: 10 M 3 2 + 10 M 1 2 = M 3 2 v 1 + 2 M v 2 1 2 3 2 v 1 + 2 v 2 = 5 ( 3 + 2 ) … (1) Along y -axis: - 10 M 1 2 + 10 M 1 2 = M v 1 1 2 - 2 M v 2 1 2 v 1 2 - 2 v 2 = 5 ( 2 - 1 ) … (2) From equations (1) and (2) v 1 3 2 + 1 2 = 5 3 + 2 + 5 ( 2 - 1 ) v 1 = 13.02 m / s v 2 = 5 3 + 5 2 - 13.02 × 3 2 2 = 19.72 m s - 1

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