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Question
A body is weighed by a spring balance to be 1.000 kg at the North Pole. How much will it weigh at the equator? Account for the earth's rotation only.
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Solution
Let gp be the acceleration due to gravity at the poles.
Let ge be the acceleration due to gravity at the equator.
Now, acceleration due to gravity at the equator is given by ge = gp \[-\] ω2r
= 9.81 − (7.3 × 10−5)2 × 6400 × 103
= 9.81 − (53.29 × 10−10) × 64 × 105
= 9.81 − 0.034 = 9.776 m/s2
Now, mge = 1 kg × 9.776 m/s2
= 9.776 N
∴ The body will weigh 9.776 N at the equator.
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