### Video Transcript

Evaluate the magnitude of gravitational force between two 5.0-kilogram mass spherical steel balls separated by a center-to-center distance of 15 centimeters.

In this problem, weโll assume that capital ๐บ, the universal gravitational constant, is exactly 6.67 times 10 to the negative 11th meters cubed per kilogram second squared.

Letโs start by highlighting some of the vital information given to us. Weโre told the mass of each of the spherical steel balls, which is 5.0 kilograms.

Weโre also told that they have a center-to-center distance of 15 centimeters. We want to solve for the magnitude of the gravitational force between them. Weโll call this ๐น sub ๐.

To begin, letโs recall the relationship telling us the gravitational force magnitude between two masses, called ๐ sub one and ๐ sub two. The gravitational force magnitude between two masses is equal to ๐บ, the gravitational constant, multiplied by the product of the masses, ๐ one times ๐ two, divided by the distance between them squared.

Recall that capital ๐บ is equal to 6.67 times 10 to the negative 11th meters cubed per kilogram second squared. Letโs apply this equation for gravitational force to our scenario. The problem statement tells us that ๐ one and ๐ two are the same, that they both equal 5.0 kilograms.

Weโre also told that the distance between the centers of the spherical steel balls is 15 centimeters, which is equal to 0.15 meters.

We can now enter in the values for ๐บ, ๐ one, ๐ two, and ๐ into this equation for force magnitude. And we find an equation that reads the gravitational force magnitude is equal to 6.67 times 10 to the negative 11th meters cubed per kilogram second squared multiplied by 5.0 kilograms times 5.0 kilograms divided by 0.15 meters squared.

When we calculate this value, we find it equal to 7.4 times 10 to the negative 8th newtons. This is the gravitational force magnitude between these two masses.