A satellite moving in a circular path of radius `r` around earth has a time period `T`. If its radius slightly increases by `4%`, then percentage change in its time period is

Options

A. `3/2(T/r)Deltar`
B. `(T/r)Deltar`
C. `3/2((T^(2))/(r^(2)))Deltar`
D. `3/2((T^(2))/r)Deltar`

Answer

A

Explanation

According to Kepler's `II` law, `T^(2)alphaR^(3)` differentiable on both sides w.r.t. `r`
`(DeltaT)/T=3/2((Deltar)/r)`