The mean radius of earth is R, its angular speed on its own axis is w and the acceleration due to gravity at earth's surface is g. What will be the radius of the orbit of a geostationary satellite

Options

A. `(R^(2) g // omega^(2) )^(1//3)`
B. `(Rg // omega^(2) )^(1//3)`
C. `(R^(2) omega^(2) // g )^(1//3)`
D. `(R^(2) g // omega )^(1//3 )`

Answer

A

Explanation

T = `(2pi r)/(v_(0)) = (2pi r)/((gR^(2)//r)^(1//2)) = (2pi r^(3//2))/(sqrt(gR^(2))) = (2pi)/(omega)`
Hence, `r^(3//2) = (sqrt(gR^(2)))/(omega) or r^(3) = (gR^(2))/(omega^(2))`
or , r = `(gR^(2) // omega^(2))^(1//3)`