An aluminium and steel rod having same length | vedclass

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(B) Given: Total length $L = 120 \ cm$ at $30^{\circ} C$. Since they have the same length, $\ell_0 = 60 \ cm$ for each rod.Change in temperature $\Del

Vedclass · Accepted Answer

$120.15$

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(B) Given: Total length $L = 120 \ cm$ at $30^{\circ} C$. Since they have the same length, $\ell_0 = 60 \ cm$ for each rod.Change in temperature $\Delta T = 100^{\circ} C - 30^{\circ} C = 70^{\circ} C$.Coefficient of linear expansion for aluminium $\alpha_A = 24 	imes 10^{-6} /{ }^{\circ} C$.Coefficient of linear expansion for steel $\alpha_S = 1.2 	imes 10^{-5} /{ }^{\circ} C = 12 	imes 10^{-6} /{ }^{\circ} C$.The final length of the composite rod is the sum of the final lengths of the individual rods:$\ell_{	ext{final}} = \ell_0(1 + \alpha_A \Delta T) + \ell_0(1 + \alpha_S \Delta T)$$\ell_{	ext{final}} = \ell_0 [2 + (\alpha_A + \alpha_S) \Delta T]$$\ell_{	ext{final}} = 60 [2 + (24 	imes 10^{-6} + 12 	imes 10^{-6}) 	imes 70]$$\ell_{	ext{final}} = 60 [2 + (36 	imes 10^{-6}) 	imes 70]$$\ell_{	ext{final}} = 60 [2 + 0.00252] = 120 + 0.1512 = 120.1512 \ cm$.Rounding to two decimal places, the length is $120.15 \ cm$.

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