Question

With rise in temperature, the Young’s modulus of elasticity
A. Increases
B. Decreases
C. Remains unchanged
D. None of these

Answer 1

Young’s modulus of elasticity is the measure of elasticity and stiffness of the material. Recall the expression for Young’s modulus of elasticity and find the dependence of Young’s modulus of elasticity on the change in the length of the material. Recall the formula for linear expansion of the length of the conductor with change in temperature to answer this question.

Complete answer:
We know that Young’s modulus of elasticity or simply modulus of elasticity is the measure of elasticity of the material. In the elastic region of the material, we have seen that the change in stress is proportional to the change in strain produced in the material.

We have the formula for Young’s modulus of elasticity,
$Y = \dfrac{{FL}}{{A\,\Delta L}}$
Here, F is the stress, L is the original length of the wire, $A\,$ is the cross-sectional area of the wire and $\Delta L$ is the change in the length of the wire due to applied stress.

From the above equation, we see that the Young’s modulus of elasticity is inversely proportional to the change in length of the wire. Therefore, we can say that the Young’s modulus of elasticity is the measure of stiffness of the material.

We know the expression for linear expansion or compression of the material with the change in temperature,
$\Delta L = L\,\alpha \,\Delta T$
Here, L is the original length of the wire, $\Delta L$ is the change in the length of the wire, $\,\alpha$ is the coefficient of linear expansion and $\Delta T$ is the change in temperature.

Therefore, from the above equation, with increase in temperature, the length of the wire increases and since the Young’s modulus of elasticity is inversely proportional to the change in the length, the Young’s modulus decreases with the rise in temperature.

Therefore, the correct answer is option B.

Note: The Young’s modulus is a measure of stiffness of the material. With rise in temperature, the length of the material increases which decreases its stiffness. Thus, we can say that with rise in the temperature, the Young’s modulus decreases.