Question

How much less would you weigh on the top
of Mount Everest (elevation 8850 m) than at
sea level? The value of the universal gravita-
tional constant is 6.67 × 10−11 N · m2/kg2.

Answer 1

Gravitational attraction
F = G m₁m₂/r²
G = 6.67e-11 m³/kgs²
m₁ and m₂ are the masses of the two objects in kg
r is the distance in meters between their centers (center of mass)
earth radius 6,371,000 m
earth mass 5.97e24 kg

M is mass of earth, m is your mass
∆F = [ G m₁m₂/r² ] – [ G m₁m₂/r² ]
∆F/m = (GM) [( 1/r² ) – ( 1/(r+8850)² )]

∆F/m = (3.98e14) [(2.463683e-14) – (2.456852e-14)]
∆F/m = (3.98e14) [6.83e-17)]
∆F/m = 0.0272
but this is change in weight / mass
weight = mass x 9.8

∆F/F = 0.0272/9.8 = 0.00278 or 0.278% (2)