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(D) The thermal strain that would occur if the wire were free to contract is given by $\Delta L / L = \alpha \Delta T$. Here,$\alpha = 10^{-5} \ K^{-1

Vedclass · Accepted Answer

$40$

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(D) The thermal strain that would occur if the wire were free to contract is given by $\Delta L / L = \alpha \Delta T$. Here,$\alpha = 10^{-5} \ K^{-1}$ and $\Delta T = 100^{\circ} C - 0^{\circ} C = 100 \ K$. So,$\Delta L / L = 10^{-5} 	imes 100 = 10^{-3}$. Since the wire is prevented from contracting,the stress developed is equal to the Young's modulus multiplied by the strain: $	ext{Stress} = Y 	imes (\Delta L / L)$. $	ext{Stress} = 10^{11} 	imes 10^{-3} = 10^8 \ N \ m^{-2}$. Stress is also defined as force per unit area,so $	ext{Stress} = F / A = (mg) / A$. Equating the two expressions for stress: $mg / A = 10^8$. $m = (10^8 	imes A) / g = (10^8 	imes 4 	imes 10^{-6}) / 10$. $m = 400 / 10 = 40 \ kg$.

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