Motion in Straight Line

Question

Where the acceleration due to gravity on the surface of earth is (i) maximum (ii) minimum? Find the difference in the maximum and minimum value of g on the surface of the earth.

Solution

The acceleration due to gravity on the surface of the earth at angle of latitude $space straight lambda$ is,

$straight g subscript straight lambda equals straight g minus Rω squared cos squared straight lambda$
(i) The value of g is maximum at points where
$cos squared straight lambda equals 0 space or space straight lambda equals 90 degree.$
Thus, acceleration due to gravity is maximum at poles.
∴ $straight g subscript max equals straight g subscript straight p equals straight g minus Rω squared cos squared 90 degree equals straight g$
(ii) The value of g is minimum at points where
 $cos squared straight lambda equals 1 space or space straight lambda space equals space 0 degree.$
Thus, acceleration due to gravity is minimum at the equator.
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The difference in the value of g at pole and equator is,
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$equals left parenthesis 6.4 cross times 10 to the power of 6 right parenthesis space open parentheses fraction numerator 2 straight pi over denominator 86400 end fraction close parentheses squared$
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