Question

Within elastic limit, prove that Young’s modulus of material of wire is the stress required to double the length of wire.

Answer 1

(i) Let, L = Initial length of wire

2 L = Final length of wire

∴ Increase in length = ∆l = 2L – L = L

(ii) Longitudinal strain of wire = \(\frac{\triangle l}{L}=\frac{L}{L}=1\)

(iii)

∴ Y = Longitudinal stress

(iv) Hence, Young’s modulus of material of wire is the stress required to double the length of wire.