A satellite can be in a geostationary orbit around earth at a distance r from the centrer. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around if its distance from the centre is

Options

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

Answer

C

Explanation

Let angular velocity is `omega rArr mr omega^(2)=(GMm)/(r^(2))`
`omega^(2)=(GM)/(r^(3))` so `omega_(1)^(2)r_(1)^(3)=omega_(2)^(2)r_(2)^(3)`
`r_(2)^(3)=r_(1)^(3)((omega_(1))/(omega_(2)))^(2) rArr r_(2)^(3)=(r_(1)^(3))/(4) rArr r_(2)=(r_(1))/(4^(1//3))`