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If a satellites is revolving close to a ...

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`

Text Solution

Verified by Experts

The correct Answer is:
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)`
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