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))

What should be the length of a day on the earth when a body has no app

1.	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» Solution :Weight mg of a body acts towards the centre of the earth. If the radius of the earth is R, at the EQUATORIAL region, the centrifugal FORCE experiencedby the body is `m omega^(2)` R, where, `omega` is the angular velocity of the earth about its own axis. 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, mg = m`omega^(2)` R or,` "" omega = sqrt((g)/(R))` So, length of a day = time period of rotation of the earth (T) ` = (2pi)/(omega) = 2pi sqrt((R)/(g)) = 2pi xxsqrt( (6400 xx 10^(3))/(9.8) ) =` 5077.6 s = 1 h 24.6 min.