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 × 10^{24} kg

Radius at equator is, R_{e} = 6378000 m

Radius at pole is, R_{p} = 6357000 m

At the equator, weight, W_{e} = GMm/R_{e} ^{2}

At the pole, weight, W_{p} = GMm/R_{p} ^{2}

Change in weight = W_{p} – W_{e} = GMm(1/R_{p} ^{2} – 1/R_{e} ^{2})

So, % change in weight is = (W_{p} – W_{e})/W_{e} × 100 %

= GMm(1/R_{p} ^{2} – 1/R_{e} ^{2})/[GMm/R_{e} ^{2}] × 100 %

= (R_{e} ^{2})(1/R_{p} ^{2} – 1/R_{e} ^{2}) × 100 %

Putting the values we get = 0.66%

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