Two wires of same nature and dimension have lengths 1 : 3 to produce the same amount of extension in them the required ratio of forces F1:F2 will be

Explanation

The correct answer is 3 : 1. When two wires of the same material and cross-sectional area have lengths in the ratio 1:3, the force required to produce the same extension is inversely proportional to their lengths. Therefore, the longer wire (3 times the length of the shorter one) requires 3 times more force to reach the same extension. This is why the ratio of forces F1:F2, where F1 is the force on the shorter wire, and F2 is the force on the longer wire, is 3:1. The other options incorrectly suggest either a lesser force is required for the longer wire or propose a non-linear relationship between force and length.