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

Answer

C

Explanation

For a geo = stationary satellite
`T prop (1)/(omega)`
`T^(2) prop r^(2)`
`:. (1)/( omega^(2)) prop r^(2)` As `omega _("earth") ` is doubled So r will be `(1)/(2^(2//3)) = (1)/(4^((1//3)))` times