A lauching vehicle carrying an artificial satellite of mass `m` is set for launch on the surface of the earth of mass `M` and radius `R`. If the satellite intended to move in a circular orbit of radius `7R`, the minimum energy required to be spent by the launching vehicle on the satellite is

Options

A. `(GMm)/R`
B. `-(13GMm)/(14R)`
C. `(GMm)/(7R)`
D. `-(GMm)/(14R)`

Answer

B

Explanation

`E_(1)=(GMm)/R` (at the surface)
`E_(2)=(GMm)/(14R)` (in the orbit)
Eergy required `E=E_(1)-E_(2)`
`=(-13GMm)/(14R)`