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Two wires A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratio

1. 2 : 1
2. 1 : 4
3. 1 : 8
4. 8 : 1

Correct answer: 8 : 1

Solution

The increase in length is proportional to the applied force and inversely proportional to the cross-sectional area and directly proportional to the length. Since the lengths are in the ratio 1:2 and diameters in the ratio 2:1, the cross-sectional areas are in the ratio 4:1. Thus, the increase in length will be in the ratio (1/4) × 2 = 1:8.

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