These both situation is truely shown in graph (D) A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of `g_0` , the value of acceleration due to gravity at the earth's surface, is

Options

A. `(2mg_0R^2)/(R+h)`
B. `-(2mg_0R^2)/(R+h)`
C. `(mg_0R^2)/(2(R+h))`
D. `-(mg_0R^2)/(2(R+h))`

Answer

D

Explanation

`implies` Total energy of satellites revoleve around earth .
`U = -(GM_em)/(2r)`
`:. U = - (GM_e_m)/(2(R+h)) " "...(1) " " [ :. r = R + h]`
Now `g_0 = (GM_e)/R^2`
`:. GM_e = g_0R^2`
In equ. (1) `GM_e = g_0 R^2`
`U = -(mg_0R^2)/(2(R+h))`