You put a 50 kg object on a bathroom scale at the North Pole, and the scale read

Question

You put a 50 kg object on a bathroom scale at the North Pole, and the scale reads exactly 50 kg (actually, it measures the force FN that the scale exerts on the object, but displays a reading in kg). At the North Pole you are 6357 km from the center of the Earth. At the equator, the scale reads a different value due to two effects:

(1) The Earth bulges out at the equator (due to its rotation), and you are 6378 km from the center of the Earth.

(2) You are moving in a circular path due to the rotation of the Earth (one rotation every 24 hours).

Taking into account both of these effects, how does the scale reading at the equator compare with the scale reading at the North Pole?

Explanation / Answer

The value of g at different latitudes is well established and well measured. At sea level, the the effective (measured) value of g:

g (At 0* -at equator) = 9.78039 m/sec^2

g (90* -at North pole) = 9.83217 m/sec^2

Thus you weigh more on the pole...
The difference in g values is about 0.05178 m/sec^2

thus using the above fact we get

weight at equator=10*9.78039/9.83217=9.947kg

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