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The mean radius of the earth is R, its a...

The mean radius of the earth is `R`, its angular speed on its own axis is `omega` and the acceleration due to gravity at earth's surface is `g`. The cube of the radius of the orbit of a geo-stationary satellite will be

A

`R^2g//omega`

B

`R^2omega^2//g`

C

`Rg//omega^2`

D

`R^2g//omega^2`

Text Solution

Verified by Experts

The correct Answer is:
D
`v_0=sqrt((GM)/r)`
`rArrv_0=sqrt((gR^2)/r)rArr(romega)^2=(gR^2)/rrArrr^3=(gR^2)/(omega^2)`
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