In a wire of length L, the increase in its length is l. If the length is reduced to half, the increase in its length will be

Explanation

When the length of the wire is halved, the increase in its length (strain) under the same force will also be halved. Strain is proportional to the original length, so reducing the length by half results in a proportional reduction in the extension. Thus, the increase in length becomes l/2. Option A is incorrect as it does not account for the change in original length. Option B is incorrect because it incorrectly suggests the increase would double rather than halve. Option D is incorrect because Option C accurately describes the situation.ΔL = (FL) / (AY)Given:Original ΔL = l, original length = LIf the length is reduced to half (L' = L/2), and other factors remain constant:ΔL' = (F(L/2)) / (AY)= (1/2) × (FL) / (AY)= (1/2) × lSo, the increase in length will be l/2.