5. A bowling ball (mass = 7.2 kg, radius = 0.13 m) and a billiard ball (mass = 0.45 kg, radius =

0.028 m) may each be treated as uniform spheres. What is the magnitude of the maximum
gravitational force that each can exert on the other?

To calculate the magnitude of the maximum gravitational force that each ball can exert on the other, we can use the equation for gravitational force:

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

where:
F is the gravitational force
G is the gravitational constant (approximately 6.67 x 10^-11 Nm^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects

First, let's calculate the distance between the centers of the two balls. Since they are assumed to be spheres, we can use the sum of their radii:

r = radius1 + radius2 = 0.13 m + 0.028 m = 0.158 m

For the bowling ball (mass = 7.2 kg) and the billiard ball (mass = 0.45 kg), let's calculate the gravitational force:

F = (6.67 x 10^-11 Nm^2/kg^2) * ((7.2 kg) * (0.45 kg)) / (0.158 m)^2

F = (6.67 x 10^-11 Nm^2/kg^2) * (3.24 kg^2) / (0.158 m)^2

F = (6.67 x 10^-11 Nm^2/kg^2) * (3.24 kg^2) / (0.025 m^2)

F = (6.67 x 10^-11 Nm^2/kg^2) * (3.24 kg^2) / 0.025 m^2

Let's calculate this value now:

F = 8.65 x 10^-9 N

Therefore, the magnitude of the maximum gravitational force that each ball can exert on the other is approximately 8.65 x 10^-9 Newtons.