Q137 / 180 · COMEDK 2023 (Memory Based) · Physics
Starting from the centre of the earth having radius $R$, the variation of $g$ (acceleration due to gravity) is shown by
- A

- Correct answerB

- C

- D

Solution
Acceleration due to gravity at a depth $d$ below the surface of the earth is given by
$\begin{aligned}
g_{\text {depth }} & =g_{\text {surface }}\left(1-\frac{d}{R}\right) \\
& =g_{\text {surface }}\left[\frac{R-d}{R}\right]=d_{\text {surface }}\left(\frac{r}{R}\right)
\end{aligned}$
Also, for a point at height $h$ above surface,
$g_{\text {height }}=g_{\text {surface }}\left[\frac{R^2}{(R+h)^2}\right]$
Therefore, we can say that value of $g$ increases from centre to maximum at the surface and then decreases as depicted in graph (b).
Hence, the correct answer is option: 'B'.