Physics - Universal Gravitation

Two small lead balls of masses and are fixed a distance apart on a laboratory bench. A student moves the larger mass toward the smaller mass so the distance is now only . After the mass was moved, by what factor did the gravitational force between the lead balls change?

Explanation

The gravitational force obeys an inverse-square law. Decreasing the distance by a factor of will increase the force by a factor of , or .

The gravitational force between two objects is . What would be the force of gravity between them if the mass of one of the objects is tripled and the distance between them is doubled?

Explanation

So the fact that we don't actually know any of the numbers doesn't matter.

What matters is we have the equation $F = G\frac{M_{1}M_{2}}{r^2}$

The masses have a direct proportional relationship with the force. That means that if a mass doubles, the force doubles.

We can also see that the radius (distance between the masses) has an inverse square relationship with Force. So if we double the radius, we divide the force by 4.

So based on the problem, we triple a mass and double the radius. So we triple the force then divide by 4.

$100N \cdot \frac{3}{4}=75N$