What is the energy required to launch a `m` kg satellite from earth's surface in a circular orbit at an altitude of 7R ? (R = radius of the earth)

Options

A. `(2)/(3) mgR`
B. `mgR`
C. `(5)/(6)mgR`
D. `(1)/(3)mgR`

Answer

C

Explanation

E = Energy of satellite - energy of satellite on surface of earth
`=-(GMm)/(2(3R))-[-(GMm)/(R)]" "{:((because,"h=2R"),( :. ,"total distance = 3R"):})`
`=(5)/(6)(GMm)/(R)=(5)/(6)mgR " "("as" (GM)/(R)=gR)`