Final Answer:
The gravitational force of attraction between two small spheres of osmium with radii 3.20 cm each and a density of 22.4 g/cm³, given the gravitational constant g = 6.67 × 10⁻¹¹ N·m²/kg², is approximately 2.04 × 10⁻⁶ N.
Step-by-step explanation:
The formula to calculate the gravitational force between two masses is F = (G * m₁ * m₂) / r², where F is the gravitational force, G is the gravitational constant (6.67 × 10⁻¹¹ N·m²/kg²), m₁ and m₂ are the masses of the two spheres, and r is the distance between their centers.
Firstly, we find the mass of each osmium sphere using the formula: mass = volume * density. The volume of a sphere is (4/3)πr³. Given the radius (3.20 cm), we calculate the volume and then the mass of one sphere, considering its density as 22.4 g/cm³.
Next, we find the total force of attraction by substituting the masses and the distance between their centers into the gravitational force formula. The distance between the centers of the spheres is the sum of their radii, which is 2 * 3.20 cm.
Finally, we calculate the gravitational force using the given values and find it to be approximately 2.04 × 10⁻⁶ N, which represents the attractive force between the two osmium spheres.
Understanding the mass of each sphere from its density, calculating the distance between their centers, and utilizing the gravitational force formula yields the final result of the gravitational force of attraction between the two osmium spheres as calculated.