Question

Consider 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 of B goes on increasing
• B. B goes on decreasing and that of A goes on increasing
• C. each decreases at the same rate
• D. each decreases at different rates

Answer 1

The correct option is D each decreases at different rates

The variation of 'g' with altitude is: $g^{\prime }=g(1-\frac{2h}{R})$
The variation of 'g' with depth is: $g^{\prime }=g(1-\frac{d}{R})$
So, from the above equations we can deduce that if a person goes deep into a mine or to a height above the Earth's surface, the gravitational field decreases at different rates.