Question

Which of the following graphs shows the variation of acceleration due to gravity $g$ with depth $h$ from the surface of the earth ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Acceleration due to gravity at depth $h$ from surface of earth,

$g_h=g(1-\frac{h}{R})$

$\Rightarrow g_h=-g\frac{h}{R}+g$

$\Rightarrow g_h=\left(\frac{-g}{R}\right)h+g........\left(1\right)$

Comparing with equation of straight line,
$y=mx+c............\left(2\right)$

comparing eq. (1) from eq. (2)

Slope, $m$ is $-ve$, intercept $c$ is $+ve$.

Thus, the most appropriate graph is

Key concept: The acceleration of due to gravity at a depth $d$ below the surface of the earth is given by $g_d=g(1-\frac{d}{R})$