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Atoms And Molecules

Question
CBSEENSC9006149

Find the percentage change in the weight of a body when it is taken from the equator to poles. The radius of the earth at the poles is 6357 km, the radius at the equator is 6378 km.

Solution

A t space t h e space p o l e s comma space space straight g subscript straight p space equals space fraction numerator G M over denominator straight R subscript straight p superscript 2 end fraction
A t space t h e space e q u a t o r comma space straight g subscript straight e space equals space fraction numerator G M over denominator straight R subscript straight e superscript 2 end fraction

R a t i o space i s space g i v e n space b y comma

therefore space space straight g subscript straight p over straight g subscript straight e space equals space open parentheses straight R subscript straight e over straight R subscript straight p close parentheses squared space

space space space space space space space space space space space space space space space equals space open parentheses 6378 over 6357 close parentheses squared space

space space space space space space space space space space space space space space space equals left parenthesis 1.0033 right parenthesis squared space

space space space space space space space space space space space space space space space equals space 1.0066

i. e. comma space space straight g subscript straight p space equals space 1.0066 space straight g subscript straight e 
The percentage increase in weight the body is taken from the equator to the poles,
                      space fraction numerator m g subscript straight p space minus space m g subscript straight e over denominator m g subscript straight e end fraction cross times 100 space equals space fraction numerator straight g subscript straight p space space minus space straight g subscript straight e over denominator straight g subscript straight e end fraction cross times 100
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 1.006 space straight g subscript straight e space minus space straight g subscript straight e over denominator straight g subscript straight e end fraction cross times space 100
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 0.0066 space cross times space 100 space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 0.66 space percent sign space space asymptotically equal to space space space 0.7 space percent sign.