a)
The acceleration due to gravity at a certain location on Earth is given by
where
G is the gravitational constant
M is the Earth's mass
R is the Earth's radius
h is the altitude above the Earth's surface
At the top of Mt. Everest,
R = 6380 km =
With
(1)
At the Earth's surface,
R = 6380 km =
h = 0
g = ?
So
(2)
By doing the ratio (2)/(1), we find an expression for g in terms of g':
And therefore,
b) 519.3 N
The weight of an object near the Earth's surface is given by
where
m is the mass of the object
g is the acceleration of gravity at the object's location
In this problem,
m = 50 kg is the mass of the object
g' = 9.77 m/s^2 is the acceleration of gravity on top of Mt Everest
Susbtituting,