If two rods of lengths L and 2L,having coeffi | vedclass

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(D) The change in length for the first rod is $\Delta L_1 = \alpha \Delta T L$. The change in length for the second rod is $\Delta L_2 = (2\alpha) \De

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$\frac{5\alpha}{3}$

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(D) The change in length for the first rod is $\Delta L_1 = \alpha \Delta T L$. The change in length for the second rod is $\Delta L_2 = (2\alpha) \Delta T (2L) = 4\alpha \Delta T L$. Since the rods are connected end-to-end,the total change in length is $\Delta L_{net} = \Delta L_1 + \Delta L_2 = \alpha \Delta T L + 4\alpha \Delta T L = 5\alpha \Delta T L$. The total length of the composite rod is $L_{total} = L + 2L = 3L$. For the composite rod,$\Delta L_{net} = \alpha_{eff} \Delta T L_{total}$. Substituting the values,$5\alpha \Delta T L = \alpha_{eff} \Delta T (3L)$. Solving for $\alpha_{eff}$,we get $\alpha_{eff} = \frac{5\alpha}{3}$.

If two rods of lengths $L$ and $2L$,having coefficients of linear expansion $\alpha$ and $2\alpha$ respectively are connected end-to-end,then find the average coefficient of linear expansion of the composite rod.

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