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Question
The temperature of a wire is doubled. The Young’s modulus of elasticity ______.
Options
will also double.
will become four times.
will remain same.
will decrease.
Solution
The temperature of a wire is doubled. The Young’s modulus of elasticity will decrease.
Explanation:
Young's modulus (Y): It is defined as the ratio of normal stress to longitudinal strain within the limit of proportionality.
`Y = "Normal stress"/"Longitudinal strain"`
= `(F/A)/((ΔL)/L)`
= `(FL)/(AΔL)`
The fractional change in length of any material is defined as `(ΔL)/L_0 = αΔT` where ΔT is the change in the temperature, L0 is the original length, α is the coefficient of linear expansion of the given material and L0 is the original length of material.
So, simply a change in length is due to change in temperature.
`ΔL = L_0αΔT`
And Young's modules
(Y) = `"Stress"/"Strain"`
= `(FL_0)/(A xx ΔL)`
= `(FL_0)/(AL_0 ΔT) ∝ 1/(ΔT)`
As Y ∝ 1/∆T
When temperature increases ∆T increases, hence Y decreases.
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