Ncert Exercises & Solutions

The temperature of the wire is doubled. Young's modulus of elasticity:

1.	will also double.	2.	will become four times.
3.	will remain the same.	4.	will decrease.

Hint: \( \text { Young's modulus (Y)}=\frac{\text { Stress }}{\text { Strain }}\)

Step: Find Young's modulus.
We know that with an increase in temperature, the length of a wire changes as;
\(\Rightarrow {L}=L_{0}(1+\alpha \Delta {T})\)
where \(\Delta T \) is the change in temperature, \(L_0\) is the original length, \(\alpha\) is the coefficient of linear
expansion and \(L \) is the length at the temperature \(T.\)
Then, \(\Delta {L}={L}-{L}_0={L}_0 \alpha \Delta {T}\)
The Young's modulus of elasticity is given by;
\(\Rightarrow \text { Young's modulus (Y)}=\frac{\text { Stress }}{\text { Strain }}=\frac{F L_0}{A \times \Delta L}=\frac{{FL}_0}{{AL}_0 \alpha \Delta {T}} \propto \frac{1}{\Delta {T}}\)
Since \(\text{Y} \propto \frac{1}{\Delta T},\) Young's modulus decreases with an increase in temperature.
Hence, option (4) is the correct answer.

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