What effect does increasing the weight force have on the extension of a string?

When the weight force acting on a string is increased, the extension of the string also increases. This is a manifestation of Hooke's Law, which states that the extension of a spring or string is directly proportional to the force applied, as long as the elastic limit of the material is not exceeded.

In this scenario, as more weight is added, the gravitational force pulls down on the string, causing it to stretch further. The relationship between the force (weight) and extension is linear and can be expressed through the equation F = kx, where F is the force applied, k is the spring constant, and x is the extension.

As long as the material remains within its elastic limit (the range where it can return to its original shape once the force is removed), increasing the weight will lead to a corresponding increase in extension. This clear relationship makes the increase in extension upon adding weight the correct and logical conclusion.