Acceleration Due to Gravity question from JEE Main 2021 (31 Aug, Shift 2)

Answer: (d)

1. $g_{\text{depth}} = g\left(1 - x\right)$ and $g_{\text{height}} = \frac{g}{(1+x)^2}$, with $x = \frac{r}{R_E}$.
2. Ratio $= (1 - x)(1 + x)^2 = (1 - x)(1 + 2x + x^2)$
3. $= 1 + x - x^2 - x^3$
4. So the answer is (d) $1 + \frac{r}{R_E} - \frac{r^2}{R_E^2} - \frac{r^3}{R_E^3}$.