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Motion In Straight Line

Question
CBSEENPH11017592

When a body of mass m is taken from latitude λ1 to λthen how much its weight will change? 

Solution
The acceleration due to gravity gλ at any angle of latitude is given by, 
                         straight g subscript straight lambda equals straight g minus Rω squared cos squared straight lambda 
Weight of mass m at latitude straight lambda subscript 1 is m 
                       straight W subscript 1 equals straight m left parenthesis straight g minus Rω squared space cos squared straight lambda subscript 1 right parenthesis 
At latitude straight lambda subscript 2, weight of mass is, 
                      space space straight W subscript 2 equals straight m left parenthesis straight g minus Rω squared cos squared straight lambda subscript 2 right parenthesis 
Change in weight is, 
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   space space space space space space space space space space equals mRω squared left parenthesis cos squared straight lambda subscript 1 minus cos squared straight lambda subscript 2 right parenthesis