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 GM m)/(14R )`
C. `(GMm)/(7R)`
D. `(GMm)/(14R)`

Answer

B

Explanation

The energy of artificial satellite at the surface of the earth
`E_(1)=(GMm)/(R )`
when the satellite is intended to move in a circular orbit of radius 7R then energy of artifical satellite
`E_(2)=-1/2 (GMm)/(7R)`
The minimum enegy required
`E=E_(1)-E_(2)=-(GMm)/(R )+1/2(GMm)/(7R)`
`=(-14GMm+GMm)/(14R)=(-13 G?Mm)/(14 R)`