Energy required to move a body of mass m from an orbit of radius 2R to 3R

Energy required to move a body of mass m from an orbit of radius 2R to 3R is

  1. (GMm)/(3R2)
  2. (GMm)/(6R)
  3. (GMm)/(8R)
  4. (GMm)/(12R2)

Solution

The two orbits will have different gravitational potential energies. Energy required to move from one orbit to another is equal to change in gravitational potential energy.

Gravitational PE of a body is given by (-GMm)/r

PE at r = 2R, E1 = (-GMm)/(2R)

PE at r = 3R, E2= (-GMm)/(3R)

Therefore energy required to change the orbit is E2 - E1 = (GMm)/(6R)

The correct option is B.