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 peakin Antarctica? The product GM Earch =3.99*1014N*m2*kg-1, the radius of theEarth is 6.38*106m, and the height above sea level ofthe Vinson Massif is 5.15*103m. Neglect the flatteningof the Earch 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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