If the distance between two objects is reduced by a factor of 10, how will Fg be affected?

10 Times greater

100 Times Greater

10 Times less

100 Times less

Second option: 100 times greater.

Explanation:

Fg means gravitational attraction force.

The gravitational attraction force is ruled by Newton's law of universal gravitation.

This law states that between two objects there is force of attraction that is directly proportional to the product of their both masses and invsersely related to the square of the distance between them.

The mathematical expression of the law is:

Fg = G m₁ m₂ / d²

Where:

Fg is the gravitational attraction force, G is the gravitational universal constant, m₁ and m₂ are the masses of the objects, and d is the distance between the two objects.

So, since the distance is squared, when the distance is reduced by a factor of 10, the denominator is reduced by a factor of 10², which is 100.

When the denominator is reduced by a factor, the quotient is multiplied by such factor, so the force will be multiplied by 100.

Doing the product Gm₁m₂ equal to a constant factor k and d₂ = d / 10, you get this expression:

Fg₂ = k / d₂² = k / (d/10) ² = k / (d² / 100) = 100 * k / d² = 100 * Fg

Hence, is is proved that the new force, Fg₂ will be 100 times greater.