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A wire of length 'L' and radius 'r' is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by 'ℓ'. Another wire of same material of length '2L' and radius '2r' is pulled by a force '2f'. Then the increase in its length will be:

1. 4ℓ
2. ℓ/2
3. 2ℓ
4. ℓ

Correct answer: ℓ

Solution

The increase in length of a wire under tension is proportional to the force applied and inversely proportional to its cross-sectional area and length. In this case, the second wire has double the length and quadruple the cross-sectional area, which balances the effect of doubling the force, resulting in the same increase in length as the first wire.

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