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)`.

Options

A. `1.1xx10^(-3)` rad/s
B. `0.83xx10^(-3)` rad/s
C. `0.63xx10^(-3)` rad/s
D. `0.28xx10^(-3)` rad/s

Answer

C

Explanation

`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)`