A satellite is revolving round the earth in an orbit of radius r with time period T. If the satellite is revolving round the earth in an orbit of radius `r + Deltar(Deltar lt lt r)` with time period `T + DeltaT(DeltaT lt lt T)` then.

Options

A. `(Delta T)/(T) = (3)/(2) (Delta r)/(r)`
B. `(Delta T)/(T) = (2)/(3) (Delta r)/(r)`
C. `(Delta T)/(T) = (Delta r)/(r)`
D. `(Delta T)/(T) = - (Delta r)/(r)`

Answer

A

Explanation

Since,`T^(2) = Kr^(3)`
Differentiating the above equation
`rArr 2 (Delta T)/(T) = 3 (Delta r)/(r) rArr (Delta T)/(T) = (3)/(2) (Delta)/(r)`