What kind of relation exists between kinetic energy `(E_k)` and orbital radius (r) of the satellite revolving around the earth?

Options

A. `E_k prop r `
B. `E_k prop r^2`
C. `E_k prop 1/r`
D. `E_k prop 1/r^2`

Answer

C

Explanation

`implies` Centripetal force for revoloving statellitte = Gravitational force
`(mv^2)/(r) = (GM_em)/r^2`
`:. 1/2 mv^2 = (GM_em)/(2r)`
`:. E_k = ((GM_em)/2).1/r`
`:. E_k prop 1/r [ :. (GM_em)/2 ` is cosntant ]