Two satellites revolve around the ‘Sun’ as shown in the figure. First satellite revolves in a circular orbit of radius R with speed v₁. Second satellite revolves in elliptical orbit, for which minimum and maximum distance from the sun are $\frac{R}{3} and \frac{5 R}{3}$ respectively. Velocities at these positions are v₂ and v₃ respectively. The correct order of speeds is

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v₂ > v₃ > v₁

v₃ < v₂ < v₁

v₂ > v₁ > v₃

v₂ > v₃ = v₁

answer is B.

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Detailed Solution

$V_{1} = \sqrt{\frac{GM}{R}}$ (orbital velocity in circular path)
For elliptical orbit
conservation of angular momentum ${mV}_{2} \frac{R}{3} = \frac{5 R}{3} {mV}_{3}$
conservation of energy $- \frac{GMm}{R / 3} + \frac{1}{2} {mV}_{2}^{2} = \frac{- GMm}{5 R / 3} + \frac{1}{2} {mV}_{3}^{2}$
Solving $V_{2} = \sqrt{\frac{5 GM}{R}} and V_{3} = \sqrt{\frac{GM}{5 R}}$