# Find the percentage change in the weight of a body when it is taken fom equator to poles. the polar radius is 6,357 Km and equatorial radius is 6,378 Km.

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%

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