Question

If mean radius of earth is R, its angular velocity is ro and the acceleration due to gravity at the surface of the earth is g, then the cube of the radius of the orbit of satellite will be ____________.

Options

• `("R"^2"g")/omega^2`

• `("R"^2"g")/omega`

• `("R"^2omega^2)/"g"`

• `("Rg")/omega^2`

Answer 1

9If mean radius of earth is R, its angular velocity is ro and the acceleration due to gravity at the surface of the earth is g, then the cube of the radius of the orbit of satellite will be `("R"^2"g")/omega^2`.

Explanation:

`omega = (2pi)/"T" = (2pi"v")/(2pi"r") = "v"_"c"/"r"`

`omega = 1/"r" xx sqrt(("GM")/"r") = sqrt(("GM")/"r"^3`

`r^3 = "GM"/omega^2 = ("gR"^2)/omega^2`