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Time period of revolution of a satellite...

Time period of revolution of a 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

`3sqrt(3)T`

Text Solution

Verified by Experts

The correct Answer is:
A
Centripetal force `mRomega^(2)=` gravitational force `=(GmM)/(R^(2))`
`omega^(2)=(GM)/(R^(3))=Gxx(4)/(3)(piR^(3).rho)/(R^(3))=G.(4)/(3)pirho`
`rArr " " 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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