Question

If a satellites is revolving close to a planet of density `rho` with period `T`, show that the quantity `rho T^(2)` is a universal constant.
A. `4 pi^(2) G`
B. `4 pi^(2)//G`
C. `3 pi//G`
D. `1//G`

Answer 1

Correct Answer - C
`upsilon = sqrt(g R)` and `T = (2pi R)/(upsilon) = (2piR)/(sqrt gR)`
or `T = (2piR)/(sqrt(Gm//R)) = 2pi sqrt((R^(3))/(G(4)/(3) pi R^(3) rho))`
`T^(2) rho = 4 pi^(2) xx (3)/(4Gpi) = (3pi)/(G)`