Question

A body is weighed by a spring balance to be 1.000 kg at the north pole. How much will it weigh at the equator ? Account for the earth's rotation only.

Answer 1

Let g be the acceleration due to gravity at equation and that of pole = g.
$g={\omega }^{2}r=9.81-(7.3\times {10}^{-5}{)}^2\times 6400\times {10}^3=9.81-(53.29\times {10}^{-10})\times 64\times {10}^5=9.81-0.034=9.776m/s^2=9.773Nor0.997kg$
The body will weight 0.997 kg at equator.