A steel rod of diameter 1 cm is clamped firmly at each end when its temperature is 25^∘ C so th

step 1 Hello students in this question we have a steel rod having diameter D equals to one centimeter a

A steel rod of diameter 1 cm is clamped firmly at each end...

A steel rod of diameter $1 \mathrm{~cm}$ is clamped firmly at each end when its temperature is $25^{\circ} \mathrm{C}$ so that it cannot contract on cooling. The tension in the rod at $0^{\circ} \mathrm{C}$ is : $\left(\alpha=10^{-5} /{ }^{\circ} \mathrm{C}, Y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$ (a) $4000 \mathrm{~N}$ (b) $7000 \mathrm{~N}$ (c) $7400 \mathrm{~N}$ (d) $4700 \mathrm{~N}$

A steel rod of diameter $1 \mathrm{~cm}$ is clamped firmly at each end when its temperature is $25^{\circ} \mathrm{C}$ so that it cannot contract on cooling. The tension in the rod at $0^{\circ} \mathrm{C}$ is :
$\left(\alpha=10^{-5} /{ }^{\circ} \mathrm{C}, Y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$
(a) $4000 \mathrm{~N}$
(b) $7000 \mathrm{~N}$
(c) $7400 \mathrm{~N}$
(d) $4700 \mathrm{~N}$

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Key Concepts

Thermal Stress in Constrained Structures

Thermal stress arises when the natural expansion or contraction of a material due to temperature changes is restricted by external constraints. In such cases, the inability of the material to expand or contract freely leads to the development of internal stresses. This concept is key in engineering applications where temperature variations occur, requiring the design to accommodate or resist the resulting stresses.

Elastic Behavior and Young's Modulus

Elastic behavior describes the property of a material to return to its original shape after the removal of an applied force, as long as the elastic limit is not exceeded. Young's modulus is a measure of this elastic stiffness; it defines the ratio of stress to strain in the elastic region of the material's stress–strain curve. This concept is essential for understanding how forces and deformations are interrelated in materials.

Thermal Expansion

Thermal expansion is the tendency of materials to change in physical dimensions in response to a change in temperature. It is quantified by the coefficient of linear expansion, which relates the change in length to the original length and the change in temperature. When a material cools down, it naturally contracts, and when it is heated, it expands.

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