Q 11-07-155JEE MainJEE Main 2021 (26 Feb, Shift 2)Medium
In the reported figure of earth, the value of acceleration due to gravity is same at point $A$ and $C$ but it is smaller than that of its value at point $B$ (surface of the earth). The value of $OA : AB$ will be $x : 5$. The value of $x$ is
Numerical value type. Enter your answer.
Answer: 4
Point $C$ is at height $h = 3200$ km $= R/2$ above the surface:
$$g_C = \frac{g}{(1 + h/R)^2} = \frac{g}{(3/2)^2} = \frac{4g}{9}$$
Point $A$ is at depth $d$: $g_A = g\left(1 - \dfrac{d}{R}\right)$.
$g_A = g_C \Rightarrow 1 - \dfrac{d}{R} = \dfrac{4}{9} \Rightarrow d = \dfrac{5R}{9}$.
$AB = d = \dfrac{5R}{9}$ and $OA = R - d = \dfrac{4R}{9}$, so $OA : AB = 4 : 5$, i.e. $x = 4$.
Solution by Sreeraj P, M.Sc Physics