At what distance will the force of attraction between two bodies weighing 1 ton each be equal to 6.67 * 10 ^ -9 N?

Given:

m1 = m2 = 1 ton the mass of two bodies;

F = 6.67 * 10 ^ -9 Newton – the force of attraction (gravitational interaction) of two bodies.

It is required to determine r (meter) – at what distance between the bodies the force of attraction will be F.

Let’s convert the units of measurement of mass to the SI system:

m1 = m2 = 1 ton = 1 * 1000 = 1000 kilograms.

Then, the distance between the two bodies will be equal to:

r = (G * m1 * m2 / F) ^ 0.5, where G = 6.67 * 10-11 N * m2 / kg2 is the gravitational constant.

r = (6.67 * 10 ^ -11 * 1000 * 1000 / (6.67 * 10 ^ -9)) ^ 0.5;

r = (6.67 * 10 ^ -5 / (6.67 * 10 ^ -9)) ^ 0.5 = (104) ^ 0.5 = 10 ^ 2 = 100 meters.

Answer: the distance between two bodies will be equal to 100 meters.