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If the earth has no rotational motion, t...

If the earth has no rotational motion, the weight of a person on the equation is W. Detrmine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight `(3)/(4)` W. Radius of the earth is 6400 km and g = 10 `m//s^(2)`.

A

`1.1xx10^(-3)` rad/s

B

`0.83xx10^(-3)` rad/s

C

`0.63xx10^(-3)` rad/s

D

`0.28xx10^(-3)` rad/s

Text Solution

Verified by Experts

The correct Answer is:
C
`w'=w-momega^2R`
`rArr 3/4w=w-m(w^2Rxxg)/g rArr omega=sqrt(g/(4R))=sqrt((10)/(4xx6400xx10^3))`
`rArr w=10/(2xx8) xx10^(-3) rads^(-1) rArr omega=.63xx10^(-3)rads^(-1)`
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