The modulus of the force of gravitational interaction of two homogeneous balls is 0.23nN.

The modulus of the force of gravitational interaction of two homogeneous balls is 0.23nN. what is the distance between their centers if the masses of the balls are 5 kg and 5.8 kg. gravitational constant 6.67 * 10 (-11)

Given:

F = 0.23 nN = 0.23 * 10 ^ -9 Newton – the force of gravitational interaction between two balls;

m1 = 5 kilograms – the mass of the first ball;

m2 = 5.8 kilograms – the mass of the second ball;

G = 6.67 * 10 ^ -11 N * m2 / kg2 – gravitational constant.

It is required to determine r (meter) – the distance between the centers of the balls.

To determine the distance, you must use the following formula (the law of universal gravitation):

F = G * m1 * m2 / r ^ 2, from here we find that:

r = (G * m1 * m2 / F) ^ 0.5 = (6.67 * 10 ^ -11 * 5 * 5.8 / (0.23 * 10 ^ -9)) ^ 0.5 = (193 , 43 * 10 ^ -11 / (0.23 * 10 ^ -9)) ^ 0.5 = (841 * 10 ^ -2) ^ 0.5 = 8.41 ^ 0.5 = 2.9 meters.

Answer: The distance between the centers of the balls is 2.9 meters.