How do you calaculate Young's Modulus without a length?

Question

An elastic string of cross-sectional area of 4 mm2 requires a force of 2.8 N to increase it's length by one tenth. Find the Young modulus for the string.

Answer 1

E=S/H where E is Young's modulus, S(tensile stress)=F/A, H(tensile strain)=e/l
E = 2.8/(4 x 10^-6 x 1/10)
=7 x 10^6 Nm^-2
let say l=1m, then e=1/10 m, i know your problem, the value of length will cancel out finally.

Answer 2

Since the formula shows that the length units cancel out, just pick a unit length Y = F dL / A L becomes Y = F 0.1 / A 1 and with the rest of your numbers 2.8x.1 / 4 mm2 x 1 or 0.28/4 or 0.7 N/mm2 or 0.0007 kN/mm2
" Some use an alternative unit form, kN/mm², which gives the same numeric value as gigapascals." in link below

Answer 3

You don't need the actual lengths. You only need the relative increase in length:

epsilon = DeltaL/L = 0.1 (one tenth)

Now Hooke's Law states:

epsilon = sigma/E,

where

sigma = F/S

is the mechanical stress, and E is Young modulus, so we have

epsilon = sigma/E => E = sigma/epsilon

E = F/(S*epsilon) = 2.8 N/(4 x 10^(-6) m2 x 10^(-1)) =
= 7.0 x 10^6 Pa = 7.0 MPa

Answer 4

assume that the length is l
the extension is therefore 0.1 l

strain=e/l = 0.1l /l =0.1

stress=F/A = 2.8/(4*10^-6)

then use young modulus=stress/strain

sorry i don't have a calculator in hand but i guess that's enough to solve the problem