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A satellite is seen after each 8 hours over equator at a place on the earth when its sense of rotation is opposite to the earth. The time interval after which it can be seen at the same place when the sense of rotation of earth and satellite is same will be

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8 hours

12 hours

24 hours

6 hours

answer is C.

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Detailed Solution

Given $8 = \frac{2 π}{ω_{1} + ω_{2}} = \frac{2 π}{\frac{2 π}{T_{1}} + \frac{2 π}{T_{2}}}, T_{1} = 24$ hours for earth.

$\Rightarrow T_{2} = 12 hours$ ( $T_{2}$ being the time period of satellite, it will remain same as the distance from the centre of the earth remains constant).

$\Rightarrow T = \frac{2 π}{ω_{2} - ω_{1}} = \frac{2 π}{\frac{2 π}{T_{2}} - \frac{2 π}{T_{1}}} = 24 hours$

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