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

Answer

B

Explanation

The energy of artificial satellite at the source of the earth
`E_(1)= -(GMm)/(R)`
When the satellite is intended to move in a circular orbit of radius 7R, then energy of artificial satellite, `E_(1)=-(1)/(2)(GMm)/(7R)`
The minimum energy required,
`E=E_(1)-E_(2)=-(GMm)/(R)+(1)/(2)((GMm)/(7R))`
`=(-14GMm+GMm)/(14 R)=-(13 GMm)/(14 R)`.