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Q. No.A metal rod of Young's modulus \(Y\) and coefficient of thermal expansion \(α \) is held at its two ends such that its length remains invariant. If its temperature is raised by
1. \(\dfrac{αt}{Y}\)
2. \(Yαt\)
3. \(\dfrac{Y}{αt}\)
4. \(\dfrac{1}{Yαt}\)
Subtopic: Thermal Stress |
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A compressive force \(F\) is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by \(\Delta{T}.\) The net change in its length is zero. Let \(l\) be the length of the rod, \(A\) its area of cross-section, \(Y\) is Young's modulus and \(\alpha\) is coefficient of linear expansion. Then, the force \(F\) is equal to:
1. \(\dfrac{{AY}}{\alpha \Delta{T}}\)
2. \({A}Y\alpha \Delta {T}\)
3. \(l^2 {Y}\alpha \Delta {T} \)
4. \(l {A}{Y} \alpha\Delta{T} \)
1. \(\dfrac{{AY}}{\alpha \Delta{T}}\)
2. \({A}Y\alpha \Delta {T}\)
3. \(l^2 {Y}\alpha \Delta {T} \)
4. \(l {A}{Y} \alpha\Delta{T} \)
Subtopic: Thermal Stress |
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Two uniform rods, \(AB\) and \(BC,\) have Young's moduli of \(1.2~\times~ 10^{11}~ \text{N/m}^2\) and \(1.5~\times~ 10^{11}~ \text{N/m}^2,\) respectively. The coefficient of linear expansion for rod \(AB\) is \(1.5~\times~ 10^{-5} /^\circ \text{C}.\) If both rods have equal cross-sectional area, then the coefficient of linear expansion of \(BC,\) for which there is no shift of the junction at all temperatures, is:
| 1. | \(1.5~\times~ 10^{-5} /^\circ \text{C}\) | 2. | \(1.2~\times~ 10^{-5} /^\circ \text{C}\) |
| 3. | \(0.6~\times~ 10^{-5} /^\circ \text{C}\) | 4. | \(0.75~\times~ 10^{-5} /^\circ \text{C}\) |
Subtopic: Thermal Stress |
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