Two satellites $S_{1}$ and $S_{2}$ are revolving in circular orbits around a planet with radius $R_{1}=3200~\mathrm{km}$ and $R_{2}=800~\mathrm{km}$ 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 $x=$

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Gravitation

Two satellites

S_{1}

and

S_{2}

are revolving in circular orbits around a planet with radius

R_{1} = 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 =

Answer: 2

Solution

For a satellite in circular orbit, the orbital speed is given by

v = \frac{GM}{r}

, where

r

is the orbital radius.

For the two satellites:

\frac{v _{1}}{v _{2}} = \frac{R _{2}}{R _{1}} = \frac{800}{3200} = \frac{1}{4} = \frac{1}{2}

Since the ratio is

\frac{1}{x}

, we have

x = 2

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Integer answer

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