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JEE Main2018PhysicsGravitationActual

A body of mass m is moving in a circular orbit of radius R about a planet of mass M . At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R 2 . And the other mass, in a circular orbit of radius 3 R 2 . The difference between the final and the initial total energies is

Options

  1. A+ G m 6 R
  2. B- G m 2 R
  3. C- G m 6 R
  4. DG m 2 R

Correct answer

C. - G m 6 R

Step-by-step solution

E i = - G M m 2 R , E f = - G M m / 2 2 R 2 - G M m / 2 2 3 R 2 = - G M m 2 R - G M m 6 R = - 4 G M m 6 R = - 2G M m 3 R E f - E i =   G M m 2 R - 2 3 + 1 2 =   - G M m 6 R .  

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