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Time period of revolution of a nearest s...

Time period of revolution of a nearest satellite around a planet of radius R is T . Period of revolution around another planet, whose radius is 3R but having same density is

A

T

B

3T

C

9T

D

`3sqrt3T`

Text Solution

Verified by Experts

The correct Answer is:
A
Centripetal force `mRomega^2` = gravitational force `= (GmM)/R^2`
`omega^2=(GM)/R^3=Gxx4/3(piR^3.rho)/R^3=G.4/3pirho`
`implies omega = sqrt((4piGrho)/3)" or " (2pi)/T = sqrt((4piGrho)/3)`
As, T does not depend on R. Hence, T remains unchanged.
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