Two objects attract each other gravitationally with a force of 2.1×10−10 when they are 0.25 apart. Their total mass is 4.50 .

You also have omitted the dimensions that go with the force and mass numbers. Numbers without dimensions are useless in physics and many other disciplines.

You can use the numbers provided to derive Newton's gravitational constant G. (This was done in the Cavendish experiment)

To calculate the mass of each object, we can use the formula for gravitational force:

F = G * (m1 * m2) / r^2,

where F is the gravitational force between the two objects, G is the gravitational constant (approximated as 6.67430 × 10^-11 N m^2 / kg^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers.

In this case, we know that the gravitational force (F) between the two objects is 2.1 × 10^-10 N, the distance between them (r) is 0.25 m, and their total mass (m1 + m2) is 4.50 kg.

Let's solve the equation step by step:

1. Rearrange the formula to solve for (m1 * m2):
(m1 * m2) = (F * r^2) / G.

2. Substitute the given values into the formula:
(m1 * m2) = (2.1 × 10^-10 N * (0.25 m)^2) / (6.67430 × 10^-11 N m^2 / kg^2).

3. Calculate the expression on the right side of the equation:
(m1 * m2) = (2.1 × 10^-10 N * 0.0625 m^2) / (6.67430 × 10^-11 N m^2 / kg^2).

Simplifying further:
(m1 * m2) = 3.9375 × 10^-12 kg.

4. Since we know that the total mass (m1 + m2) is 4.50 kg, we can rewrite the equation as:
(m1 + m2) * (m1 * m2) = (m1 + m2) * 3.9375 × 10^-12 kg.

Simplify further:
4.50 kg * (m1 * m2) = (m1 + m2) * 3.9375 × 10^-12 kg.

5. Now we substitute (m1 * m2) = 3.9375 × 10^-12 kg:
4.50 kg * (3.9375 × 10^-12 kg) = (m1 + m2) * 3.9375 × 10^-12 kg.

6. Simplify the equation:
17.71875 × 10^-12 kg^2 = (m1 + m2) * 3.9375 × 10^-12 kg.

7. Divide both sides of the equation by 3.9375 × 10^-12 kg:
(m1 + m2) = (17.71875 × 10^-12 kg^2) / (3.9375 × 10^-12 kg).

Simplifying further:
(m1 + m2) = 4.5 kg.

8. Therefore, the mass of each object can be calculated as:
m1 = m2 = (m1 + m2) / 2 = 4.5 kg / 2 = 2.25 kg.

So, each object has a mass of 2.25 kg.