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The radii of circular orbits of two satellites A and B of the earth, are 4R and R

The radii of circular orbits of two satellites A and B of the earth, are 4R and R respectively. If the speed of satellite A is 3 V, then the speed of satellite B will be

Options

(a) 3 V / 4
(b) 6 V
(c) 12 V
(d) 3 V / 2

Correct Answer:

6 V

Explanation:

Orbital velocity of a satellite in a circular orbit of radius a is given by
v = √(GM / a) ⇒ v α √(1/a) ⇒ v₂ / v₁ = √(a₁ / a₂)
v₂ = v₁ √(4R / R) = 2 v₁ = 6 V

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