Find the binding energy of a satellite of mass `m` in orbit of radius `r`, (R = radius of earth, g = acceleration due to gravity)

Options

A. `(mgR^(2))/(r )`
B. `(mgR^(2))/(2r )`
C. `-(mgR^(2))/(r )`
D. `-(mgR^(2))/(2r )`

Answer

B

Explanation

Binding energy is equal to negative value of total mechanical energy of a satellite the energy required to remove the satellite from its orbit around the earth to infinity is called binding energy of the satelite it is equal tonegative of total mechanical energy of satellite in its orbit
thus binding energy `=-E=(GMm)/(2r)`
but `g=(GM)/(R^(2))`
`rarr GM=gR^(2)` or `BE=(gmR^(2))/(2r)`