Two satellites are launched simultaneously into orbits of radius R and 4R. At an instant the two satellites are on the same radial line in the same direction. The time after which they have maximum separation is : (mass of earth $= M_{e}$ )

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$π \sqrt{\frac{R^{3}}{G M_{e}}}$

$\frac{8 π}{7} \sqrt{\frac{R^{3}}{G M_{e}}}$

$\frac{7 π}{8} \sqrt{\frac{R^{3}}{G M_{e}}}$

$7 π \sqrt{\frac{R^{3}}{G M_{e}}}$

answer is A.

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Detailed Solution

$θ = ω_{1} t θ + π = ω_{2} t π = (ω_{2} - ω_{1}) t t = \frac{π}{ω_{2} - ω_{1}} a n d ω = \sqrt{\frac{G M}{r^{3}}}$

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