Question:medium

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

Updated On: Mar 19, 2026
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Correct Answer: 2

Solution and Explanation

The speed of a satellite in a circular orbit is determined by the gravitational force acting as the centripetal force. The formula for the speed v of a satellite is:
v=√(GM/R)
where G is the gravitational constant, M is the mass of the planet, and R is the radius of the orbit from the center of the planet. For two satellites, S1 and S2, with radii of orbits R1=3200 km and R2=800 km respectively, their speeds are:
v1=√(GM/R1)
v2=√(GM/R2)
The ratio of speeds v1 to v2 is:
v1/v2=(√(GM/R1))/(√(GM/R2))
=√(R2/R1)
Substitute R1=3200 km and R2=800 km:
v1/v2=√(800/3200)=√(1/4)=1/2
Thus, the ratio is 1/2, meaning x=2.
The computed value x falls within the range [2, 2]. Therefore, x=2.
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