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.

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Solution

Let ‘m’ be the mass of a body.
Mass of earth is, M = 5.9721 × 10²⁴ 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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