Q 11-07-063JEE MainJEE Main 2024 (5 Apr, Shift 2)Medium
A satellite revolving around a planet in a stationary orbit has a time period of 6 hours. The mass of the planet is one-fourth the mass of the earth. The radius of the orbit around the planet is (Given: radius of the geostationary orbit for earth is $4.2\times10^4\ \text{km}$)
Answer: (B) $1.05\times10^4\ \text{km}$
$T^2 = \dfrac{4\pi^2r^3}{GM} \Rightarrow r^3 \propto MT^2$.
$$\frac{r^3}{r_E^3} = \frac14\times\left(\frac{6}{24}\right)^2 = \frac{1}{64} \Rightarrow r = \frac{r_E}{4} = \frac{4.2\times10^4}{4} = 1.05\times10^4\ \text{km}$$
Solution by Sreeraj P, M.Sc Physics