A body at rest relative to the surface of the earth rotates with the earth and therefore...

A body at rest relative to the surface of the earth rotates with the earth and therefore moves in a circular path about the polar axis of the earth considered fixed. Derive an expression for the ratio k of the apparent weight of such a body as measured by a spring scale at the equator (calibrated to read the actual force applied) to the true weight of the body, which is the absolute gravitational attraction to the earth. The absolute acceleration due to gravity at the equator is g = 9.815 m/s2. The radius of the earth at the equator is R = 6378 km, and the angular velocity of the earth is ω = 0.729(10^-4) rad/s. If the true weight is 100 N, what is the apparent measured weight