Two objects attract each other gravitationally with a force of 2.1×10−10 when they are 0.21 apart. Their total mass is 4.00 .

This is not a question. You have also failed to provide the units of force, distance and mass. Are they Newtons, meters and kilograms?

The force that the objects exert upon each other depends upon the product of the two masses, NOT the sum of the masses.

If your statement were true and you provided the mass of both objects, the statement could be used to calculate the gravitational constant G. Is that what you were asked to do?

Uhm, this is a question.

first of all you use the equation F=Gm1m2/r^2, knowing that m1+m2 = 4.00
you re-arrange the formula to be m1m2=Fr^2/G
plug in and solve

To solve this problem, we can use Newton's law of universal gravitation, which states that the force of gravity between two objects is given by:

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

Where:
- F is the gravitational force between the two objects
- G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2 / kg^2)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects

In this case, we have the following information:
- The gravitational force between the objects is 2.1 × 10^-10 N
- The distance between the objects is 0.21 m
- The total mass of the two objects is 4.00 kg

To find the mass of each object individually, we can use the fact that the total mass is the sum of the masses of the two objects:

m1 + m2 = 4.00 kg

Now, let's solve for the mass of each object.

First, rearrange the equation to solve for the individual masses:

m1 = 4.00 kg - m2

Now substitute this expression into the equation for the gravitational force:

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

2.1 × 10^-10 N = (6.67430 × 10^-11 N m^2 / kg^2) * [(4.00 kg - m2) * m2] / (0.21 m)^2

Simplify the equation:

2.1 × 10^-10 N = (6.67430 × 10^-11 N m^2 / kg^2) * (4.00 kg * m2 - m2^2) / (0.21 m)^2

Now, multiply both sides of the equation by (0.21 m)^2 to eliminate the denominator:

(0.21 m)^2 * 2.1 × 10^-10 N = (6.67430 × 10^-11 N m^2 / kg^2) * (4.00 kg * m2 - m2^2)

0.0441 N m^2 = (6.67430 × 10^-11 N m^2 / kg^2) * (4.00 kg * m2 - m2^2)

Now, simplify the equation further:

0.0441 N m^2 = (26.6972 × 10^-11 N m^2 / kg^2) * (4.00 kg * m2 - m2^2)

Now, rearrange the equation to form a quadratic equation:

0.0441 N m^2 - (26.6972 × 10^-11 N m^2 / kg^2) * (4.00 kg * m2 - m2^2) = 0

Solve this equation for m2 using the quadratic formula:

m2 = [-b ± sqrt(b^2 - 4ac)] / (2a)

Where:
a = -(26.6972 × 10^-11 N m^2 / kg^2)
b = 0
c = 0.0441 N m^2

Solving this equation will give you the values of m2. From there, you can find m1 by substituting the value of m2 into the equation m1 = 4.00 kg - m2.

Note that there may be two possible solutions for m2, as indicated by the ± in the quadratic formula.