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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

A body of mass 2 m moving with velocity v makes a head-on elastic collision with another body of mass m which is initially at rest. Loss of kinetic energy of the colliding body (mass 2 m ) is

Options

  1. A1 9 of its initial kinetic energy
  2. B1 6 of its initial kinetic energy
  3. C1 2 of its initial kinetic energy
  4. D8 9 of its initial kinetic energy

Correct answer

D. 8 9 of its initial kinetic energy

Step-by-step solution

Initial K . E of ball of mass 2 m = K 1 = 1 2 × 2 m × v 2 = m v 2 Collision is elastic so both K . E and momentum are conserved. Let velocities of balls are v 1 and v 2 after collision. So, K E is conserved 1 2 2 m v 2 = 1 2 2 m v 1 2 + 1 2 m v 2 2 ⇒ v 2 = v 1 2 + 1 2 v 2 2 2 ( v 2 − v 1 2 ) = v 2 2 .... ( i ) And, momentum is conserved 2 m v + m 0 = 2 m v 1 + m v 2 ⇒ 2 v = 2 v 1 + v 2 ... (ii) Now, v 2 = 2 v - v 1 From (i) 2 ( v 2 − v 1 2 ) 2 ( v − v 1 ) = v 2 2 v 2 v + v 1 = v 2 v − v

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