A steel rod with Y = 2.0 times 10^{11} , N/m^ | vedclass

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Question

(A) When a rod is prevented from expanding due to heating,a thermal stress is developed in it.The thermal force $F$ is given by the formula: $F = Y A

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(A) When a rod is prevented from expanding due to heating,a thermal stress is developed in it.The thermal force $F$ is given by the formula: $F = Y A \alpha \Delta T$.Here,$Y = 2.0 	imes 10^{11} \, N/m^2$,$A = 10 \, cm^2 = 10 	imes 10^{-4} \, m^2 = 10^{-3} \, m^2$,$\alpha = 10^{-5} \, ^\circ C^{-1}$,and $\Delta T = 400^\circ C - 0^\circ C = 400^\circ C$.Substituting the values into the formula:$F = (2.0 	imes 10^{11}) 	imes (10^{-3}) 	imes (10^{-5}) 	imes (400)$$F = 2.0 	imes 10^{11} 	imes 10^{-8} 	imes 400$$F = 2.0 	imes 10^3 	imes 400$$F = 800 	imes 10^3 \, N = 8 	imes 10^5 \, N$.Comparing this with $x 	imes 10^5 \, N$,we get $x = 8$.

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