Let E be the energy required to raise a satellite to height `h` above earth's surface and E' be the energy required to put the same satellite into orbit at that height. Then `E//E'` is equal to

Options

A. `(2h)/((R+2h))`
B. `(2h)/((2R+3h))`
C. `(R)/(R+h)`
D. `(2R)/(2h+R)`

Answer

A

Explanation

`E=Delta U=(mgh)/(1+h//R)=(mghR)/((R+h))`
E' = energy of satellite - energy of satellite on surface of earth
`=-(GMm)/(2(R+h))-(-(GMm)/(R))`
`=mgR^(2)[(1)/(R)-(1)/(2(R+h))]=(mg(R+2h)R)/(2(R+h))`
Now, `(E)/(E')=(2h)/((R+2h))`.