Answer:
a) M = 2,939 10¹⁷ kg , b) [tex]M_{e}[/tex] / M = 2 10⁷
Explanation:
a) The equation for gravitational force is
F = G m M / r²
Where G is the gravitational constant that is worth 6.67 10⁻¹¹ N m² / kg², m the mass epa person. M the mass of the Mountain and r the distance between them.
The value of this force is 2% of the person's weight
F = 0.02 W = 0.02 mg
we replace
0.02 mg = G m M / r²
M = 0.02 g r² / G
r = 10 km = 10 10³ m = 1.0 10⁴ m
M = 0.02 9.8 (10⁴)² / 6.67 10⁻¹¹
M = 2,939 10¹⁷ kg
b) to compare the masses we find their relationship
[tex]M_{e}[/tex] / M = 5.98 1024 / 2,939 1017
[tex]M_{e}[/tex] / M = 2 10⁷
c) treating the mountain as a point object
d) The mountain is not spherical so the distance changes depending on the height of the mountain
