Question:
Define youngDefine young's modulus for a material. A wire of length L and area of cross section A is
stretched by a force of magnitude F. It is found that the length of the wire is increased by
ï¬
.
Find: ( See Lesson-8)
(i) Longitudinal stress
(ii) Longitudinal strain
(iii) Young's modulus
Answer:
Youngs Modulus -Within in the elastic limit, The ratio between longitudinal stress to longitudinal strain is called as Youngs Modulus.
Youngs Modulus (Y)=Longitudinal Stress/Longitudinal Strain
Given, area of corss-section = A
Length = L
Force= F
So, Y= (F/A) / ΔL/L
Stress = F/A
And Strain= ΔL/L
Longitudinal stress= F/A
Volume remain same even after stretching,
So, AL= A’L’
=A’(L+ ΔL)
A’=AL /(L+ ΔL)
(1) Stress = F/A’ = F/(AL/L+ ΔL)
= F(L+ ΔL)/AL
(2) Strain= ΔL/L
(3) Y= Stress/Strain = F(L+ ΔL)/AL*L/ ΔL
=F*(L+ ΔL)/A* ΔL
Y= F/A*(L/ ΔL+1)
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