Question

The magnitude of acceleration due to gravity at an altitude 'h' from the earth is equal to its magnitude at a depth 'd'. Find the relation between 'h'and 'd'. If the 'h'and 'd' both increases by $50$ %, are the magnitudes of acceleration due to gravity at the new altitude and the new depth equal.

• A. $d=h$
• B. $d=2h$
• C. $h=\frac{d}{3}$
• D. $d=4h$

Answer 1

The correct option is B $d=2h$

$g_n=g(1-\frac{2h}{R})g_d=g(1-\frac{d}{R})$

If $g_n=g_{d}g(1-\frac{2h}{R})=g(1-\frac{d}{R})\Rightarrow \frac{2h}{R}=\frac{d}{R}\therefore 2h=d$