Question

Acceleration due to gravity relation with angular frequency

Answer 1

Outward centrifugal force caused due to rotation of earth affects (decreases) the acceleration due to gravity. The change varies with the latitude.

Let us consider the earth to be a spherical ball of mass ‘M’ and radius ‘R’. An object of mass ‘m’ is at point P at latitude φ, when the earth is not rotating the weight of the object is mg. But earth is rotating with angular velocity. So, the object is moving in a circular path of radius ‘r’ as shown in the figure. The object experiences centrifugal force,

The object is being acted by two forces ‘mg’ and ‘FfFf‘. The resultant of these two forces gives the apparent weight of the object (m’g). The resultant of the two forces is given by the diagonal of the parallelogram OPAB.