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

Addition K.E.
`DeltaKE=(GMm)/(2R_1)-(GMm)/(2R_2)=U_i-U_f`
`=1/2GMm[1/(R_1)-1/(R_2)]`