1) Find the percentage change in the weight of a body when it is taken from equator to poles. The polar radius is 6357 km and eqatorial radius is 6378 km.
2) The density of ice is 918 kgm-3 and that of sea water is 1030 kgm-3. An iceberg floats with a portion 224 litres outside water. Find the value of iceberg.
3) What are the laws of flotation ? Give some illustrations.

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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_e²
At the pole, weight, W_p = GMm/R_p²
Change in weight = W_p – W_e = GMm(1/R_p² – 1/R_e²)
So, % change in weight is = (W_p – W_e)/W_e × 100 %
= GMm(1/R_p² – 1/R_e²)/[GMm/R_e²] × 100 %
= (R_e²)(1/R_p² – 1/R_e²) × 100 %
Putting the values we get = 0.66%

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