What will be the angular velocity of the diurnal motion of the earth, so that the weight of a body at the equatorial region is 0.6 of the present weight? Radius of the earth = 6400 km.

Explanation

Due to the diurnal motion of the earth, a centrifugal force acts on a body on the surface of the earth and hence the body suffers an apparent loss of weight.
Apparent weight of the body at the equatorial region
= mg - `m omega^(2)` R
(`omega` = angular velocity, R = radius of the earth)
According to the problem, 0.6 mg = mg-m`omega` R
or, `" " omega = sqrt((0.4 xx g)/(R)) = sqrt((0.4 xx 9.8)/(6400 xx 1000)) = 7.8 xx 10^(-4) "rad" cdot s^(-1)`