Final Answer:
The gravitational force of attraction between the two spheres is 1.38 × 10^5 N.
Step-by-step explanation:
The two spheres attract each other due to the gravitational force between them. The force of gravity between two objects is given by the following formula:
F = G ⋅ (m1 ⋅ m2) / r² ,
where:
F is the force of gravity
G is the gravitational constant (6.67430 × 10^-11 N m² kg^-2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
We first need to calculate the mass of each sphere. We know that the density of osmium is ρ = 22.4 g/cm³. The mass of a sphere is given by the following formula:
m = ρ ⋅ V
where:
m is the mass of the sphere
ρ is the density of the sphere
V is the volume of the sphere
The volume of a sphere is given by the following formula:
V = (4/3)πr³
where:
V is the volume of the sphere
r is the radius of the sphere
Since the two spheres are in contact, their radii are equal. The distance between the centers of the two spheres is simply the sum of their radii, which is R = 2r = 5.4 cm.
Plugging in the given values, we get:
m = (22.4 g/cm³) ⋅ ((4/3)π(2.7 cm)³) = 1.54 × 10^4 g
Therefore, the mass of each sphere is 1.54 × 10^4 g.
Plugging in all of the values, we get:
F = (6.67 × 10^{-11} N·m²/kg²) ⋅ (1.54 × 10^4 g)² / (5.40 cm)² = 1.38 × 10^5 N
Therefore, the gravitational force of attraction between the two spheres is 1.38 × 10^5 N.