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,

Options

A. `(mg_0 R^2)/(2(R + h))`
B. ` - (mg_0 R^2)/(2(R + h))`
C. `(2mg_0 R^2)/(R+ h)`
D. ` -(2mg_0 R^2)/(R+ h)`

Answer

B

Explanation

Total energy of satellite at height h from the earth surface,
`E = PE + KE = - (GMm)/((R + h)) + 1/2 mv^2` ...(i)
Also `, (mv^2)/((R + h)) = (GMm)/((R + h)^2) " or " v^2 = (GM)/(R + h)` ....(ii)
`E = - (GMm)/((R + h)) + 1/2 (GMm)/((R +h)) =- 1/2 (GMm)/((R+h))`
`= - 1/2 (GM)/(R^2) xx (mR^2)/((R+h)) = - (mg_0 R^2)/(2 (R + h)) " " ( because g_0 = (GM/(R^2))`