A metallic rod of length L and cross-sectional area A has a linear expansion coefficient alpha. A compressive force F is applied to its ends to prevent any change in length as the temperature increases by Delta T. Find the Young's modulus (Y) for this metal.

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EEJ MAIN Physics QUESTION #7053

Question 1

A metallic rod of length $L$ and cross-sectional area $A$ has a linear expansion coefficient $\alpha$. A compressive force $F$ is applied to its ends to prevent any change in length as the temperature increases by $\Delta T$. Find the Young's modulus ($Y$) for this metal.

$\frac{F}{A\alpha\Delta T}$✔️
$\frac{F}{A\alpha(\Delta T - 273)}$
$\frac{F}{2A\alpha\Delta T}$
$\frac{2F}{A\alpha\Delta T}$

Correct Answer Explanation

Thermal strain produced in the rod if it were free to expand is $\frac{\Delta L}{L} = \alpha \Delta T$.

Young's modulus is defined as $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L}$.

Substituting the thermal strain:

$Y = \frac{F/A}{\alpha \Delta T} = \frac{F}{A\alpha \Delta T}$

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