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Physics

Mechanics

Easy

Question

A satellite is seen after every 6 hours over the equator. It is known that it rotates opposite to that of earth's direction. Then the angular velocity (in radians per hour) of the satellite about the centre of earth will be:

$\frac{π}{2}$
$\frac{π}{3}$
$\frac{π}{4}$
$\frac{π}{8}$

The correct answer is: $pi over 4$

$text Let end text omega subscript E equals text angular velocity of earth, end text omega subscript S equals text angular velocity of satellite. end text text Then, end text 6 equals fraction numerator 2 pi over denominator open parentheses omega subscript E plus omega subscript S close parentheses end fraction not stretchy rightwards double arrow omega subscript E plus omega subscript S equals pi over 3 not stretchy rightwards double arrow omega subscript S equals pi over 3 minus pi over 12 open parentheses therefore omega subscript E equals fraction numerator 2 pi over denominator 24 end fraction equals pi over 12 text rad per hour end text close parentheses omega subscript S equals pi over 4 text radian per hour end text$

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