A metal bar of length $$L$$ and area of cross-section $$A$$ is clamped between two rigid supports. For the material of the rod, its Young’s modulus is $$Y$$ and the coefficient of linear expansion is $$\alpha$$. If the temperature of the rod is increased by $$\Delta t^{\circ} \mathrm{C}$$, the force exerted by the rod on the supports will be:
1. $$YAL\Delta t$$
2. $$YA\alpha\Delta t$$
3. $$\frac{YL\alpha\Delta t}{A}$$
4. $$Y\alpha AL\Delta t$$

Subtopic:  Thermal Stress |
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The temperature of a wire of length 1 meter and an area of cross-section 1cm2 is increased from $$0^{\circ} \mathrm {C}$$ to $$100^{\circ} \mathrm {C}$$. If the rod is not allowed to increase in length, the force required will be: $$(\alpha = 10^{-5}/ ^{\circ} \mathrm {C} ~\text{and} ~Y = 10^{11} ~\text{N/m}^2)$$

 1 $$10^3 \mathrm{~N}$$ 2 $$10^4 \mathrm{~N}$$ 3 $$10^5 \mathrm{~N}$$ 4 $$10^9 \mathrm{~N}$$
Subtopic:  Thermal Stress |
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A brass wire $$1.8$$ m long at $$27$$ °C is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of$$-39$$ °C, what is the tension created in a wire with a diameter of $$2.0$$ mm? (coefficient of linear expansion of brass $$=2.0 \times10^{-5}$$ K-1, Young's modulus of brass$$=0.91 \times10^{11}$$ Pa)
1. $$3.8 \times 10^3$$ N
2. $$3.8 \times 10^2$$ N
3. $$2.9 \times 10^{-2}$$ N
4. $$2.9 \times 10^{2}$$ N

Subtopic:  Thermal Stress |
67%
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