Question

A force stretches a wire by 1.0 {\rm mm}.Part 1A second wire of the same material has the same cross section andtwice the length. How far will it be stretched by the same force?(In 2 sig figs and mm)Part 2A third wire of the same material has the same length and twice thediameter as the first. How far will it be stretched by the sameforce? (In 2 sig figs and mm)

Answer 1

Step-by-step explanation:

Young's modulus of a material : Stress/Strain;

Y.M=
`(F/A)/(dl/l)`; Where F is the Force applied, A is its cross sectional area, dl is the extension, and l is the original length;

Re-arranging the formula:

dl=
`(F)/(Y.M)  * (L)/(A)`; Force and Y.M is constant.

It can be observed that extension is proportional to the original length

a) Extension of second wire is twice the extension of first wire i.e 2.0 mm

b) From the formula above, it can be observed that extension is inversely proportional to the cross sectional area. Doubling the diameter(or radius) increases the area 4 times. The new extension will be 1/4th of 1 mm i.e 0.25mm.