Two identical balls are at a distance of 0.1 m from each other and are attracted with a force of 6.67

Two identical balls are at a distance of 0.1 m from each other and are attracted with a force of 6.67 * 10 ^ -15 N. What is the mass of each ball.

Given:

m1 = m2 = m – the mass of the balls is the same;

R = 0.1 meter – the distance between the balls;

G = 6.67 * 10 ^ -11 m ^ 3 * kg ^ -1 * s ^ -2 – gravitational constant;

F = 6.67 * 10 ^ -15 Newton – the force of gravitational interaction between the balls.

It is required to find the mass of the balls m (kilogram).

According to the universal law of gravity:

F = G * m1 * m2 / R ^ 2;

F = G * m * m / R ^ 2;

F = G * m ^ 2 / R ^ 2, hence:

m = (R ^ 2 * F / G) ^ 0.5 = (0.1 ^ 2 * 6.67 * 10 ^ -15 / (6.67 * 10 ^ -11)) ^ 0.5 =

= (0.01 * 10 ^ -4) ^ 0.5 = (10 ^ -6) ^ 0.5 = 10 ^ -3 kilograms = 0.001 kilograms.

Answer: The mass of the balls is 0.001 kilograms (1 gram).