Question

Find ratio of acceleration due to gravity $g$ depth d and at height $h$, where $d=2h$.

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $1:4$

Answer 1

Answer: (A)

Acceleration due to gravity decreases both at altitude and depth.
If $g^{\prime }$ is the acceleration due to gravity at a point, at a height h above the surface of earth, and $g$ be acceleration due to gravity on earths surface, then
$g^{\prime }=g\left(1-\frac{2h}{R}\right)...(i)$
If $g$'' be the acceleration due to gravity at a point at depth $d$, below the surface of earth, then
$g^{\prime \prime }=g\left(1-\frac{d}{R}\right)....(ii)$
But $d=2h$ (given)
$\therefore g^{\prime \prime }=g\left(1-\frac{2h}{R}\right)...(iii)$
$\therefore \frac{g^{\prime \prime }}{g^{\prime }}=\frac{g\left(1-\frac{2h}{R}\right)}{g\left(1-\frac{2h}{R}\right)}=1$
$\therefore g^{\prime \prime }:g^{\prime }=1:1$
Note The value of acceleration due to gravity, also decreases due to rotation of earth.