Consider a body of mass m is placed on a weighing machine. The body is at rest with respect to earth. But earth itself is having rotational motion. Hence the body on the weighing machine also subjected to rotational motion and experiencing centripetal force towards centre of earth acting on the body.
Figure shows the three forces acting on the body placed on weighing machine
(1) W is the force earth's gravitational force which is the true weight of the body.
(2) N is the normal reaction force which is sensed by the weighing machine to measure weight .(3) \( F_C \) is centripetal force due to earths rotation.
Hence Normal force which is used for measuring the weight is (true weight W - centripetal force \( F_C \) ).
Hence measured weight reading obtained from weight measuring machine is slightly less than true weight.