# You find your mass to be 42 kg on a weighing machine

You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?

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 earthâ€™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) FC is centripetal force due to earths rotation.
Hence Normal force which is used for measuring the weight is (true weight W - centripetal force FC ).
Hence measured weight reading obtained from weight measuring machine is slightly less than true weight.
If mass is calculated from the measured weight, then mass will be slightly less.
The difference between true weight and measured weight is calculated in terms of difference (go - g) which is the difference between the acceleration due to gravity without and with centripetal force.
At equator difference in acceleration due to gravity = (go - g) = 0.034 m/s2 , when we move towards pole from equator, the difference decreases and it becomes zero at pole.