A satellite orbiting the earth in a circular orbit of radius R...

Time period of satellite $T^2=\frac{4 \pi^2}{G M} r^3 \text{\text{ or } } T^2=\frac{4 \pi^2}{g R^2} r^3 \quad\left[\because G M=g R^2\right]$ or \quad T=$\frac{2 \pi}{R} \sqrt{\frac{r^3}{g}}$ or T \propto r^{3 / 2} \therefore \quad$\frac{T_1}{T_2}=\left(\frac{r_1}{r_2}\right)^{3 / 2}$$Given,$\quad T_1=3 $\mathrm{~h},$ T_2=2$4 \mathrm{~h} (geostationary satellite)$r_1=R, r_2=36000 $\mathrm{~km}$ \therefore \quad $\frac{3}{24}$=\left(\frac{R}{36000}\right)^{3 / 2}$or \quad R=\left(\frac{1}{8}\right)^{2 / 3}$\times 36000$or$\quad R=$\frac{1}{4} \times 36000=9000 \mathrm{~km}$