**PHYSICS help**

If a metal wire has its length doubled and its diameter tripled, by what factor does its Young's modulus change?

### 3 Answers | Add Yours

The Young's modulus is a constant for metals in the range of values of stress for which Hooke's law is valid.

It can be determined by the relation: Young's modulus= Tensile Stress/ Tensile Strain.

**If the length of a wire is made double and the diameter of the wire is made triple, it does not change the Young's Modulus of the wire.** The changes made will influence the stress on the wire for the same force applied and this will alter the strain that is witnessed.

In your case as the diameter is tripled, the cross sectional area becomes nine times, so the same force applied leads to a stress that is 1/9th the original stress. Therefore the resulting strain is also 1/9 of the original strain. In terms of a change in length, let’s takes the change in length originally as L and after the alterations as L’. As the strain is now 1/9 and the length is double, so L’ = (2/9)*L.

Young's modulus is a physical property of the material of which wires or others objects may be made. It is a measure of the ability of a material to resist strain - that is, being stretched, under stress. If wire of length 'L' and area 'A' is stressed or pulled by a force 'F' stretches in length by 'l', the young modulus is calculated as:

Young's modulus = (F*l)/(L*A)

Young's Modulus is same is same for any given material irrespective of the size or shape of the products made out of it. Therefore the Young's modulus of the wire will not change by changing either its length or diameter.

However assuming that the same force is applied to the wire, then doubling the length of wire will result in the strain, or increase in length of wire, also doubling. When the diameter of the wire is tripled, the area of the wire will increase 9 times (3^2 times). This will result in strain becoming 1/9. Thus the combined effect of doubling length of wire and tripling the diameter will result in strain becoming:

Strain in second wire = (Strain in original wire)*2*1/9 = (Strain in original wire)*2/9

Young's modulus = (F*l)/(L*A)

Young's Modulus is same is same for any given material irrespective of the size or shape of the products made out of it. Therefore the Young's modulus of the wire will not change by changing either its length or diameter.

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes