• Distance between the centers of two identical spheres: 1 m


• Gravitational force between the spheres: 1 N


• Gravitational constant: G = 6.67 × 10^-11 Nm²/kg²

To calculate the mass of each sphere, we need to use Newton's law of universal gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.


The formula for gravitational force is given by:

F = (G * m₁ * m₂) / r²

Where:
- F is the gravitational force between the spheres,
- G is the gravitational constant,
- m₁ and m₂ are the masses of the spheres, and
- r is the distance between the centers of the spheres.

In this problem, the force (F) is given as 1 N, the distance (r) is given as 1 m, and the value of G is known (6.67 × 10^-11 Nm²/kg²). We need to calculate the mass of each sphere (m₁ = m₂).


Rearranging the formula, we get:

m₁ * m₂ = (F * r²) / G

Substituting the given values:

m₁ * m₂ = (1 * (1)²) / (6.67 × 10^-11)

m₁ * m₂ = 1.5 × 10^10 kg²

Since the two spheres are identical, their masses are the same, so we can write:

m₁² = 1.5 × 10^10

Taking the square root of both sides:

m₁ = √(1.5 × 10^10)

Calculating this value:

m₁ ≈ 3.87 × 10^5 kg

Therefore, each sphere has a mass of approximately 3.87 × 10^5 kg.


The mass of each sphere is approximately 3.87 × 10^5 kg. This is calculated using Newton's law of universal gravitation, where the gravitational force between the spheres is given as 1 N and the distance between their centers is 1 m. The gravitational constant (G) is known as 6.67 × 10^-11 Nm²/kg². By substituting these values into the formula and solving, we find the mass of each sphere.