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

Angular speed of earth=angular speed of geostationary satellite
`T prop1/(omega)`
`implies (T_(2))/(T_(1))=(omega_(1))/(omega_(2))=1/2 implies T_(2)=(T_(1))/2`
Also, `T prop r^(3//2)`
`:. ((r_(2))/(r_(1)))^(3//2)=(T_(2))/(T_(1))=1/2`
`(r_(2))/r_(1)=(1/2)^(2//3)=1/(4^(1//3))`
`r_(2)=(r_(1))/(4^(1//3))`