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What should be the length of a day on the earth when a body has no apparent weight at the equatorial region? (Radius of the earth = 6400 kg)or, should be the time period of rotation of the earth about its own axis so that a person on the equator feels weightless?(Equatorial radius = 6400 km,g = 9.8 mcdot s^(-2))

Answer» <html><body><p></p>Solution :Weight mg of a body acts towards the centre of the earth. If the radius of the earth is R, at the <a href="https://interviewquestions.tuteehub.com/tag/equatorial-2617989" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATORIAL">EQUATORIAL</a> region, the centrifugal <a href="https://interviewquestions.tuteehub.com/tag/force-22342" style="font-weight:bold;" target="_blank" title="Click to know more about FORCE">FORCE</a> experiencedby the body is `m omega^(2)` R, where, `omega` is the angular velocity of the earth about its own axis. <br/> When the centrifugal force acting on the body becomes equal and opposite ot the weight of the body, the apparent weight of the body becomes zero. In that case, <br/> mg = m`omega^(2)` R <br/> or,` "" omega = sqrt((g)/(R))` <br/> So, length of a day <br/> = time period of rotation of the earth (T) <br/>` = (2pi)/(omega) = 2pi sqrt((R)/(g)) = 2pi xxsqrt( (<a href="https://interviewquestions.tuteehub.com/tag/6400-330890" style="font-weight:bold;" target="_blank" title="Click to know more about 6400">6400</a> xx <a href="https://interviewquestions.tuteehub.com/tag/10-261113" style="font-weight:bold;" target="_blank" title="Click to know more about 10">10</a>^(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>))/(9.8) ) =` 5077.6 s <br/> = 1 h 24.6 min.</body></html>


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