Q85 / 90 · JEE Main 2022 (25 Jun Shift 2) · Physics

Two satellites $S_{1}$ and $S_{2}$ are revolving in circular orbits around a planet with radius $R_{I} = 3200 km$ and $R_{2} = 800 km$ respectively. The ratio of speed of satellite $S_{1}$ to the speed of satellite $S_{2}$ in their respective orbits would be $\frac{1}{x}$ where $x =$

Correct answer: 2

Solution

Orbital velocity of a satellite in circular motion around a planet,

$v_{o} = \sqrt{\frac{G M}{R}} \propto \frac{1}{\sqrt{R}}$

Now, $\frac{v_{1}}{v_{2}} = \sqrt{\frac{R_{2}}{R_{1}}} = \sqrt{\frac{800}{3200}} = \frac{1}{2}$

Hence, the value of $x = 2$ .

Hence, the correct answer is 2.