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What is the time period of rotation of t...

What is the time period of rotation of the earth around its axis so that the objects at the equator becomes weightless ?
(`g = 9.8 m//s^(2)`, Radius of earth= 6400 km)

Text Solution

Verified by Experts

g at the equator is
`g_(0) = g-g_(0) = g - R omega^(2)`
If bodies are to become weightless at the equator, `g_(0) = 0`.
`0 = g - R omega^(2) rArr R omega^(2) = g " "omega = sqrt((g)/(R))`
Time period of rotation, `T = (2pi)/(omega) = 2pi sqrt((R)/(g))`
`R = 6400 xx 10^(3)m, g = 9.8 m//s^(2)`
`T = 2pi sqrt((6.4 xx 10^(6))/(9.8)) = 5078 s = 84` minute 38s.
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