Two spheres are placed so that their centers are 2.6 meters apart. The force between the two spheres is 2.75x10^-12N What is the mass of each sphere if one sphere is twice the mass of the other sphere?

F=G2m/2.6^2 solve for m.

sorry...

F=G2M^2/2.6^2

0.28

To find the mass of each sphere, we can use the equation for the gravitational force between two objects:

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

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

Given that the force between the spheres is 2.75 x 10^-12 N and the distance between their centers is 2.6 meters, we can write the equation as follows:

2.75 x 10^-12 N = (6.67430 x 10^-11 N(m/kg)^2) * ((m1 * m2) / (2.6 m)^2)

Since one sphere is twice the mass of the other, we can express the mass of the smaller sphere as "m" and the mass of the larger sphere as "2m". Substituting these values into the equation, we get:

2.75 x 10^-12 N = (6.67430 x 10^-11 N(m/kg)^2) * ((m * 2m) / (2.6 m)^2)

Simplifying this equation further, we have:

2.75 x 10^-12 N = (6.67430 x 10^-11 N(m^2/kg^2)) * (2m^2 / (2.6 m)^2)

Now, we can solve for the mass "m" by rearranging the equation and isolating it:

m^2 = (2.75 x 10^-12 N) * (2.6 m)^2 / ((6.67430 x 10^-11 N) * 2)

m^2 = (2.75 x 2.6^2) / (6.67430 x 2 x 10^11)

m^2 ≈ 3.590572 x 10^-12 kg^2

Taking the square root of both sides, we find:

m ≈ √(3.590572 x 10^-12 kg^2)

Calculating the value, we get:

m ≈ 5.997 kg

Therefore, the mass of the smaller sphere is approximately 5.997 kg, and the mass of the larger sphere (twice the mass) would be approximately 11.994 kg.