The additional kinetic energy to be provided to a satellite of mass `m` revolving around a planet of mass `M`, to transfer it forms a circular orbit of radius `R_(1)` to another of radius `R_(2)(R_(2)gtR_(1))` is

Options

A. `GmM(1/(R_(1)^(2))-1/(R_(2)^(2)))`
B. `GmM(1/(R_(1))-1/(R_(2)))`
C. `2GmM(1/(R_(1))-1/(R_(2)))`
D. `1/2GmM(1/(R_(1))-1/(R_(2)))`

Answer

D

Explanation

`K_(1)=-(GMm)/(2R_(1)), K_(2)=-(GMm)/(2R_(2))`
`K_(2)-K_(1)=(GMm)/2(1/(R_(1))-1/(R_(2)))`