A wire is loaded by 6 kg at its one end, the increase in length is 12mm. If the radius of the wire is doubled and all other magnitudes are unchanged, then increase in length will be

Explanation

The increase in length of a wire under a load is given by the formula ΔL = (F*L) / (A*Y), where F is the force, L is the original length, A is the cross-sectional area, and Y is Young's modulus. Doubling the radius of the wire increases the cross-sectional area by a factor of four (since A = πr²). This means the increase in length, ΔL, will be reduced to a quarter of its original value, from 12 mm to 3 mm. Thus, the correct answer is 3 mm. The other options are incorrect because they do not account for the change in cross-sectional area correctly.The increase in length (ΔL) of a wire under load is given by:ΔL = (FL) / (AY)where F is the force (load), L is the original length, A is the cross-sectional area, and Y is Young's modulus.Since the radius is doubled, the cross-sectional area (A = πr2) becomes 4 times the original area.Given:Original ΔL = 12 mmNew area (A') = 4ASince ΔL ∝ 1/A, the new increase in length (ΔL') will be:ΔL' = ΔL / 4= 12 mm / 4= 3 mmSo, the increase in length will be 3 mm.