The mean radius of earth is R, its angular speed on its

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

1. (R²g / ω²)^{1 / 3}
2. (Rg / ω²)^{1 / 3}
3. (R² ω² / g)^{1 / 3}
4. (R²g / ω)^{1 / 3}

Correct Option: A

T =	2πr	=	2πr	=	2πr^{3 / 2}	=	2π
	v₀		(gR² / r)^{1 / 2}		(gR²)^{1 / 2}		ω

Hence , r^{3 / 2} =	√gR²	or r³ =	gR²
	ω		ω²

or r = (gR² / ω²)^{1 / 3}