The ratio of binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around of the earth at a height h above the earth's surface is (R = radius of the earth).

Options

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

Answer

A

Explanation

Binding energy of a satellite at rest on earth’s surface Total energy K.E. + P.E
K.E. of rotation = 0
`P. E. = - (GMm)/(R ) :. " "` Binding energy of a satellite revolving around the earth at a height ‘h’
`K.E = (GMm)/(2(R + h))`
`P. E. = - (GmM)/(2(R + h))`
Total energy = `K. E. + P. E = - (GMm)/(2(R + h)) or (B.E_1)/(B. E_2) = (2(R + h))/(R)`