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)

This question was addressed to me in an online quiz.

My query is from Gravitation in chapter Gravitation of Physics – Class 11

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).