First slide

Elastic Modulie

Question

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

Moderate

A

will also double
B

will become four times
C

will remain same
D

will decrease

Solution

We know that, with increase in temperature, length of a wire changes as $L_{t} = L_{0} (1 + αΔT)$
where, $ΔT$ is change in the temperature, L is original length, α is coefficient of linear expansion and $L_{t}$ is length at temperature T.
Now, we can write, $ΔL = L_{t} - L_{\circ} = L_{\circ} αΔT,$
Young's modulus
$(Y) = \frac{Stress}{S train} = \frac{{FL}_{\circ}}{A \times ΔL} = \frac{{FL}_{\circ}}{{AL}_{\circ} αΔT} \propto \frac{1}{ΔT}$
As, $Y \propto \frac{1}{ΔT}$
When temperature $(ΔT)$ increases, Y decreases.

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