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.

Answer 1

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.