(D) When a rod is fixed at both ends, its thermal expansion is prevented, resulting in thermal stress.Thermal strain is given by $\epsilon = \frac{\De

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(D) When a rod is fixed at both ends, its thermal expansion is prevented, resulting in thermal stress.Thermal strain is given by $\epsilon = \frac{\Delta L}{L} = \alpha \cdot \Delta T$.According to Hooke's Law, Stress $\sigma = Y \cdot \text{Strain}$.Substituting the strain value, we get $\sigma = Y \cdot \alpha \cdot \Delta T$.Since $Y$, $\alpha$, and $\Delta T$ are the factors determining the stress, the stress is independent of the length $L$ of the rod.Therefore, the correct statement is that the stress is independent of $L$.

Class 11 Physics Mechanical Properties of Solids Young’s Modulus

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$A$ metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If $L$, $\alpha$, and $Y$ denote the length of the rod, the coefficient of linear thermal expansion, and the Young's modulus of its material respectively, then for an increase in temperature of the rod by $\Delta T$, the longitudinal stress developed in the rod is

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A
inversely proportional to $\alpha$
B
inversely proportional to $Y$
C
directly proportional to $\Delta T$
D
independent of $L$

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Mechanical Properties of Solids

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Young’s Modulus

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$A$ steel wire and a copper wire are joined end to end having equal cross-sections. The elongation of the two wires is found to be equal under tension. What is the ratio of the length of the steel wire to the length of the copper wire? (Young's modulus of steel $= 2.0 \times 10^{11} \ N \ m^{-2}$ and Young's modulus of copper $= 1.1 \times 10^{11} \ N \ m^{-2}$)

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Longitudinal stress of $1\,kg/mm^2$ is applied on a wire. The percentage increase in length is $(Y = 10^{11}\,N/m^2)$. (in $\%$)

The length of an iron wire is $L$ and the area of cross-section is $A$. The increase in length is $l$ upon applying a force $F$ on its two ends. Which of the following statements is correct?

$A$ steel rod has a radius of $20\,mm$ and a length of $2.0\,m$. $A$ force of $62.8\,kN$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\,N/m^2$. The longitudinal strain produced in the wire is $..........\times 10^{-5}$.

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