A satellite can be in a geostationary orbit around earth in an orbit of radius `r`. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit aroun earth radius

Options

A. 2R
B. `( R)/(2)`
C. `( R)/(2^(1//3))`
D. `( R)/(4^(1//3))`

Answer

D

Explanation

Angular velocity `omega = (2pi)/(T)` if `omega` is doubled, T will be halved. and `T^(2)prop R^(3)` or `R^(3)prop T^(2) " " therefore R prop T^(2//3)`
`(R_(2))/(R_(1))=((T_(2))/(T_(1)))^(2//3)=((T//2)/(T))^(2//3)=((1)/(2))^(2//3)=(1)/(4^(1//3))`
`therefore R_(2)=(R_(1))/(4^(1//3)) or R'=(R )/(4^(1//3))`