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The relative uncertainty in the period o...

The relative uncertainty in the period of a satellite orbiting around the earth is `10^(-2)` . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

A

`10^(-2)`

B

`2xx10^(-2)`

C

`3xx10^(-2)`

D

`6xx10^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`Dt=10^(-2)`
`Deltar=0 m omega^2 R =(GMm)/R^2`
`rArr omega=sqrt((GM)/R^3) rArr omega^2=(GM)/R^3 2 omega d omega=G/R^3 xx dM (2domega)/omega=(dM)/M rArr (dM)/M=2xx10^(-2)`
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