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

Answer

A

Explanation

Kepler.s law can be written as follows :
`T^(2) = (4pi^(2))/(GM) r^(3)`
Relative uncertainty in the radius is negligible, hence from kepler.s law, we can write the following :
`|(Delta M)/(M)| = 2 (Delta T)/(T) = 2 xx 10^(-2)`