Question

The force (F units) between two particles is inversely proportional to the square of the

distance (x units) between them.
When the distance between two particles is x, the force is F. When the distance is reduced to
0.5x, what is the ratio of the force to the original force?

Answer 1

If the force (F units) between two particles is inversely proportional to the square of the distance (x units) between them, we can write the relationship between F and x as F = k/x^2, where k is a constant.

When the distance between the particles is reduced to 0.5x, the relationship between the new force (F') and the distance (0.5x) can be written as F' = k/(0.5x)^2.

If we divide F' by F, we find that the ratio of the new force to the original force is equal to (k/(0.5x)^2) / (k/x^2) = (1/(0.5x)^2) / (1/x^2) = (4/x^2) / (1/x^2) = 4.

Therefore, the ratio of the force to the original force when the distance between the particles is reduced to 0.5x is 4.