A wire of natural length 50 cm, diameter 1.5 mm and Young's modulus 3.2 GPa is stretched to a new length of 52.4 cm which is below the limit of proportionality How much work was done in order for this to happen?

## Step1:First, we'll calculate the change in length ΔL. That's the final stretched length of the wire subtracted from its original length. Given that the final length of the wire is and the original length is , we also need to convert the lengths from cm to m for calculating the further measurements in standard international units. ## Step2:Next, we calculate the 'strain', which is also the elongation, simply the change in length (from Step1: ) divided by the original length = = ).### ### ## Step3:Use Young's Modulus (Y) relationship for isotropic & vecrtical materials, where stress / strain = Y:### Solving for stress (σ), we have: ### Substituting into the equation values for and , we get stress .## Step4:To calculate the work done to stretch the wire, we leverage the formula:### The volume change , is merely the product of cross-sectional area multiplied by the change in length . Let's calculate the volume change:Using the given wire diameter , and noting that the radius , we substitute into the live formula for the wire/cylinder shape of the wire: (Area =π )### Finally, volume change ). Injecting this value into the work formula from before; we'll have