Question

The ratio of acceleration due to gravity at a depth h below the surface of earth and at a height h above the surface of earth for h << radius of earth

• A. Is constant
• B. Increases linearly with h
• C. Increases parabolically with h
• D. Decreases

Answer 1

The correct option is B

Increases linearly with h

Let R be the radius of earth and g the acceleration due to gravity on earth's surface.

Then the desired ration (say x) is :

$x=\frac{g(1-\frac{h}{R})}{g/{(1+\frac{h}{R})}^2}=(1-\frac{h}{R}){(1+\frac{h}{R})}^2(1-\frac{h}{R}){(1+\frac{2h}{R})}^2(h<<R)\approx 1+\frac{h}{R}$

From the expression we see that x increases linearly with h.