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NTA Abhyas JEE Main2020PhysicsGravitationPractice

Consider two identical rings of mass M and radius R fixed on a horizontal axis in a gravity-free space. A particle of mass m is held at rest at the centre of 1 st ring and projected along the axis towards 2 nd ring. The minimum speed of projection so that the particle reaches the centre of 2 nd ring is

Options

  1. AG M R
  2. B2 G M R
  3. C2 G M R 1 + 1 5 - 2
  4. DGM R 1 + 5 - 1 2

Correct answer

C. 2 G M R 1 + 1 5 - 2

Step-by-step solution

The particle should be projected such that it can reach halfway because after midpoint it will move under the attraction of 2 nd ring and will reach the center of the ring. PE i   +   KE i   =   KE f   +   PE f - GMm R - GMm 5 R + 1 2 mv 2 = - GMm 2 R × 2 v = 2 G M R 1 + 1 5 - 2

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