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Question

Two satellites S1 and S2 revolve around a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 hour and 8 hours respectively. The radius of the orbit of S1 is 104 km. When S1 is closest to S2, the angular speed of S2 as observed by an astronaut in S1 is :

A
π rad/hr
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B
π/3 rad/hr
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C
2π rad/hr
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D
π/2 rad/hr
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Solution

The correct option is B π/3 rad/hr

Angular frequency of S1
ω1=2π1 rad/hr
Angular frequency of S2
ω2=2π8 rad/hr
From kepler's law.
(T1T2)2=(R1R2)3R2R1=4
R2=4×104 km
Velocity of S1
V1=2πR11h=2π×104 km/hr
Velocity of S2
V2=2πR28h=π×104 km/hr
At closest seperation,
ω=Vrelline joininglength of line journing=V1V2R2R1
=π×104 km/hr3×104 km=π3 rad/hr

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