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 `(3R)/(2)`. The difference between the final and initial total energies is :

Options

A. `- ("GMm")/(2R)`
B. `+("GMm")/(6R)`
C. `-("GMm")/(6R)`
D. `("GMm")/(2R)`

Answer

C

Explanation

Initial gravitational potentail energy, `E_(i) = - (GMm)/(2R)`
Final gravitational potential energy,
`E_(f) = - ("GMm/2")/(2 ((R)/(2))) - ("GMm/2")/(2 ((3R)/(2))) = - ("GMm")/(2R) - ("GMm")/(6R)`
= - `(4"GMm")/(6R) = - (2"GMm")/(3R)`
`therefore `Difference between initial and final energy.
`E_(f) - E_(i) = ("GMm")/(R) ( - (2)/(3) + (1)/(2) ) = - ("GMm")/(6R)`