Question

A satellite revolves around a planet of radius “Q”. If the angular velocity of the satellite is “w” and the radius of the orbit is “4nQ”, where “n” is an integer, what is the acceleration due to gravity on the surface of the planet?

(a) (w^2 x (nQ) ^3/Q^2)

(b) 16 (w^2 x (nQ) ^3/Q^2)

(c) 64(w^2 x (nQ) ^3/Q^2)

(d) 32(w^2 x (nQ) ^3/Q^21)

Answer 1

The correct option is (c) 64(w^2 x (nQ) ^3/Q^2)

For explanation: Orbital velocity (v) = [(G x M) / (4nQ)]^1/2

(G x M) = v^2 x (4nQ)

Acceleration due to gravity (g) = (G x M) / Q^2

Therefore; g = (v^2 x (4nQ)) / Q^2

Angular velocity (w) = v/(4nQ)

v = w x (4nQ)

Therefore; g = (w^2 x (4nQ)^3/Q^2)

 = 64 x (w^2 x (nQ)^3/Q^2).