Two satellites S₁ and S₂ are revolving round a planet in coplanar and concentric circular orbits of radii R₁ and R₂ in the same direction respectively. Their respective periods of revolution are 1 hr and 8 hr. The radius of the orbit of satellite S₁ is equal to 104 km. Their relative speed when they are closest, in kmph is

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4π x 10⁴

π x 10⁴

π/2 x 10⁴

2π x 10⁴

answer is B.

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Detailed Solution

$V_{O_{1}} = \frac{R_{1} 2 π}{T_{1}}, V_{O_{2}} = \frac{R_{2} 2 π}{T_{2}}$

Relative speed = $(V_{O_{1}} - V_{O_{2}})$

$\frac{R_{1}}{R_{2}} = {(\frac{T_{1}}{T_{2}})}^{\frac{2}{3}} \Rightarrow \frac{R_{1}}{R_{2}} = {(\frac{1}{8})}^{\frac{2}{3}} \Rightarrow R_{2} = 4 R_{1}$
$V_{r e l} = 2 π (\frac{10^{4}}{1} - \frac{4 \times 10^{4}}{8})$

$= π \times 10^{4} Km / hr$

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