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What should be the period of rotation of...

What should be the period of rotation of earth so as to make any object on the equator weig half of its present value?

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The required rate be `omega`.
`F_(cp)=F_(gr)`
`mr omega^(2)=mg implies omega=sqrt((g)/(r ))`
Put `g=9.8m//sec^(2)` and `r=R=6.4xx10^(6)m` (radius of earth)
`impliesT=2pisqrt((R )/(g))=84` min (approx).
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