Question

What is the relationship between height “h” above the earth’s surface and a depth “d” below the earth’s surface when the magnitude of the acceleration due to gravity is equal? (Assume h < < R; where, R = Radius of the earth)

(a) h = d

(b) h = 2d

(c) 2h = d

(d) 3h = 2d

I had been asked this question during a job interview.

Question is taken from Acceleration due to Gravity below and above the Surface of Earth in division Gravitation of Physics – Class 11

Answer 1

Correct choice is (c) 2h = d

Easy explanation: Acceleration due to gravity above the surface of the earth;

g’ = [(G*M1)/R^2] x [1 – (2h)/R)]

Acceleration due to gravity below the surface of the earth;

g’’ = (G x M1/R^3) x (R – d)

g’ = g’’

Therefore;

[(G*M1)/R^2] x [1 – (2h)/R)] = (G x M1/R^3) x (R – d)

2h = d.