Find the percantage changeof a weight of a body when it is taken from the equator to the poles
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Let ‘m’ be the mass of a body.
Mass of earth is, M = 5.9721 × 1024 kg
Radius at equator is, Re = 6378000 m
Radius at pole is, Rp = 6357000 m
At the equator, weight, We = GMm/Re ^2
At the pole, weight, Wp = GMm/Rp ^2
Change in weight = Wp – We = GMm(1/Rp ^2 – 1/Re^2)
So, % change in weight is = (Wp – We)/We × 100 %
= GMm(1/Rp ^2 – 1/Re ^2)/[GMm/Re ^2] × 100 %
= (Re ^2)(1/Rp ^2 – 1/Re ^2) × 100 %
Putting the values we get = 0.66%
Mass of earth is, M = 5.9721 × 1024 kg
Radius at equator is, Re = 6378000 m
Radius at pole is, Rp = 6357000 m
At the equator, weight, We = GMm/Re ^2
At the pole, weight, Wp = GMm/Rp ^2
Change in weight = Wp – We = GMm(1/Rp ^2 – 1/Re^2)
So, % change in weight is = (Wp – We)/We × 100 %
= GMm(1/Rp ^2 – 1/Re ^2)/[GMm/Re ^2] × 100 %
= (Re ^2)(1/Rp ^2 – 1/Re ^2) × 100 %
Putting the values we get = 0.66%
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