Two wires of same diameter of the same material having the length L and 2L. If the force F is applied on each, the ratio of the work done in the two wires will be

Explanation

The work done on a wire is given by the expression W = (1/2) × F × ΔL, where ΔL is the change in length. For wires of the same material and cross-sectional area, ΔL is proportional to the original length when the same force is applied. Therefore, for the first wire of length L, ΔL1 = L and for the second wire of length 2L, ΔL2 = 2L. Consequently, the work done on the first wire, W1, is proportional to L, and the work done on the second wire, W2, is proportional to 2L. This gives a ratio of W1:W2 = 1:2. The other options are incorrect as they either assume an incorrect proportionality or do not account for the difference in length.