What is the difference in the weight of a 108 kg person as measuredat sea level

Question

What is the difference in the weight of a 108 kg person as measuredat sea level and at the top of the Vinson Massif, the highest peak in Antarctica ? Theproduct GMEarth=3.99 x 1014 N.m2.kg-1, the radius of the Earth is 6.38x 106 m, and the height above sea level of the Vinson Massif is 5.15 x103 m. Neglect the flattening of the Earth at the poles. Vinson Massif, the highest peak in Antarctica ? Theproduct GMEarth=3.99 x 1014 N.m2.kg-1, the radius of the Earth is 6.38x 106 m, and the height above sea level of the Vinson Massif is 5.15 x103 m. Neglect the flattening of the Earth at the poles.

Explanation / Answer

The difference between the weight of a person on different place isonly due to the acceleration due to gravity"g" because weigth is a type of a Force and by second law ofnewton we have, F = mg i.e force depend on "g". At sea level ,Acceleration due to gravity , g = 9.81m/s2 At heigth h, acceleration due to gravity , g = GM/(R +h)2 where, G = gravitaional constant M = mass of earth and GM = 3.99 x 1014 N.m2.kg-1 (given) R = radius of earth = 6.38x 106 m (given0 h = heigth of body = 5.15 x 103 m  (here) So At peak of heigth (5.15 x 103 m), Acceleration due to gravity, g' = GM/(R + 5.15 x103 )2 => g' = (3.99 x 1014 )/(6.38x 106 +5.15 x 103 )2 = (3.99 x1014 )/(4.08 x 1013 ) =>g' = 9.78 m/s2 Now,At sea level F = mg => 108 = m*9.81 => m = 108/9.81 = 11.01 kg Now, Difference in weigth = mg - mg' = m(g - g') = 11.01(9.81 - 9.78) =0.3303 N So differenc in weigth is 0.3303 N

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