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 value of $g$ measured by

• A. $A$ goes on decreasing and that by $B$ goes on increasing
• B. $B$ goes on decreasing and that by $A$ 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


For scientist $A$ which goes down in a mine
$g^{\prime }=g(1-\frac{d}{r})...\left(i\right)$

For scientist $B$, which goes up in the air
$g^{\prime }=g(1-\frac{2h}{R})...\left(ii\right)$

From equation $\left(i\right)$ & $\left(ii\right)$, it is clear that value of $g$ measured by each will decrease at different rates.

Final Answer: (d)