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 :

Options

A. `10^(-2)`
B. `2xx10^(-2)`
C. `3xx10^(-2)`
D. `6xx10^(-2)`

Answer

B

Explanation

`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)`