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Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by ΔL on applying a force F, how much force is needed to stretch the second wire by the same amount?

1. 9 F
2. 6 F
3. F
4. 4 F

Correct answer: 9 F

Solution

The force required to stretch a wire is inversely proportional to its cross-sectional area for the same material and elongation. Since the second wire has three times the cross-sectional area of the first wire, the force required will be 9 times greater to achieve the same elongation.

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