Question

Consider the earth to be a homogeneous sphere. Scientist $A$ goes deep down in a mine and scientist $B$ goes high up in a balloon. The gravitational field measured by

• A. A goes on decreasing and that by $B$ goes on increasing.
• B. Each remains unchanged
• C. $B$ goes on decreasing and that by $A$ goes on increasing.
• D. Each goes on decreasing.

Answer 1

The correct option is D Each goes on decreasing.

Variation of g with altitude is given by:

$g_{eff}=\frac{g}{{(1+\frac{h}{R})}^2}\simeq g(1-\frac{2h}{R})$

And variation of g with depth is given by:
$g_{eff}=g(1-\frac{d}{R})$

From the above two equations, it is clear that the gravitational field in both cases decreases at different rates.

Hence, Option $\left(D\right)$ is the correct answer.