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/(2sqrt2)`
C. `r/(4)^(1//3)`
D. `r/(2)^(1//3)`

Answer

C

Explanation

For a geostationary orbit the angular velocity of satellite and earth must be same
From second law,
`(GMm)/r^2 = m omega^2 r rArr r^3=(GM)/omega^2`
Now , `omega'=2omega`
And `(GMm)/(r'^2)=m omega'^2r'`
`rArr r'^3=(GM)/(omega'^2)=(GM)/((2omega)^2)=(GM)/(4omega^2) rArr r'^3=r^3/4 rArr r'=r/((4)^(1/3))`