Answer:
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.