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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

Two particles of equal mass m are moving with velocities v i ^ and v i ^ + j ^ 2 respectively. If the particles collide completely inelastically, then the energy lost in the process is

Options

  1. A3 m v 2 4
  2. B2 m v 2 3
  3. Cm v 2 3
  4. Dm v 2 8

Correct answer

D. m v 2 8

Step-by-step solution

Conserving momentum mv i ^ + m v 2 i ^ + v 2 j ^ = 2 m v 1 i ^ + v 2 j ^ On solving v 1 = 3 v 4 and v 2 = v 4 Change in K.E. 1 2 mv 2 + 1 2 m v 2 2 2 - 1 2 ( 2 m ) 9 v 2 16 + v 2 16 = 3 mv 2 4 - 5 mv 2 8 = mv 2 8

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