Question

At a point outside the Earth and a distance of x from its centre, the Earth’s gravitational field strength is 5 N kg^-1. At the Earth’s surface, the field strength is about 10 N kg^-1. Which of the following gives an approximate value for the radius of the Earth?

A) x/5

B) x/2√2

C) x√2

D) x/√2

Answer

At point x, the gravitational field strength is given by the formula:

At the surface of the Earth, the gravitational field strength is given by the formula:

Since g_s ≈ 2 g_x,

Hence, the answer is D.