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Two satellites S₁ and S₂ are revolving in circular orbits around a planet with radii R₁=3200 km and R₂=800 km respectively. The ratio of the speed of satellite S₁ to the speed of satellite S₂ in their respective orbits would be 1/x, where x is ______.

Asked in JEE Main 25th June 2nd Shift 2022 · Orbital velocity

Answer: 2

Step-by-step solution

Orbital speed falls off with distance as v=√(GM)/R, so v∝1/(√R).

Therefore (v₁)/(v₂)=√(R₂)/(R₁)=√(800)/(3200).

√1/4=1/2, so the outer satellite is the slower one.

Matching with 1/x gives x=2.

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