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

Answer

c

Explanation

Let angular velocity is `omegaimpliesmromega^(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)impliesr_(2)^(3)=(r_(1)^(3))/4impliesr_(2)=(r_(1))/(4^(1//3))`