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Physics

Mechanics

Easy

Question

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 :

8 hours
12 hours
24 hours
6 hours

The correct answer is: 24 hours

$text Given end text 8 equals fraction numerator 2 pi over denominator omega subscript 1 plus omega subscript 2 end fraction equals fraction numerator 2 pi over denominator fraction numerator 2 pi over denominator T subscript 1 end fraction plus fraction numerator 2 pi over denominator T subscript 2 end fraction end fraction comma T subscript 1 equals 24 text hours for earth. end text not stretchy rightwards double arrow T equals fraction numerator 2 pi over denominator omega subscript 2 minus omega subscript 1 end fraction equals fraction numerator 2 pi over denominator fraction numerator 2 pi over denominator T subscript 2 end fraction minus fraction numerator 2 pi over denominator T subscript 1 end fraction end fraction equals 24 text hours end text$

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