Q 11-07-060JEE MainJEE Main 2024 (4 Apr, Shift 2)Easy
The correct formula for the height of a satellite from the earth's surface is ($T$ = period, $R$ = radius of earth)
Answer: (B) $\left(\dfrac{T^2R^2g}{4\pi^2}\right)^{1/3} - R$
$T^2 = \dfrac{4\pi^2r^3}{GM}$ with $GM = gR^2$:
$$r^3 = \frac{T^2gR^2}{4\pi^2} \Rightarrow h = r - R = \left(\frac{T^2R^2g}{4\pi^2}\right)^{1/3} - R$$
Solution by Sreeraj P, M.Sc Physics