The extension in a string is ______ ______ to the weight force applied.

The extension in a string is directly proportional to the weight force applied due to Hooke’s Law. This law states that, within the elastic limit of a material, the force exerted on the material is directly proportional to the extension or compression that it experiences. This means if you double the weight force applied to the string, the extension will also double, provided the material remains within its elastic limit.

This relationship is fundamental in understanding how materials respond to forces and is critical in applications involving springs and elastic materials, where calculating extension based on applied force is essential. It emphasizes that as long as the material is not stretched beyond its elastic limit, the two quantities will maintain this linear relationship.