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  • A lead rod of length 60 cm joined at n en to an aluminium rod of length 120 cm. All measurement reer to 20o C. The coeicient o inear expansion of iron and aluminium are lead <img alt="=

A lead rod of length 60 cm joined at n en to an aluminium rod of length 120 cm. All measurement reer to 20o C. The coeicient o inear expansion of iron and aluminium are lead = 30 \times 10^{-6}/^{o}C and Al= 24 \times 10^{-6}/^{o}C then the average coefficient of the compoite system is .
 

Option: 1

36 \times 10^{-6} /{ }^{\circ} \mathrm{C}


Option: 2

20 \times 10^{-6} /{ }^{\circ} \mathrm{C}


Option: 3

28 \times 10^{-6} /{ }^{\circ} \mathrm{C}


Option: 4

25 \times 10^{-6} /{ }^{\circ} \mathrm{C}


Answers (1)

best_answer

\begin{aligned} \Delta l &=\Delta l_{1}+\Delta l_{2} \\ l \alpha \Delta T &=l_{1} \alpha_{1} \Delta T+l_{2} \alpha_{2} \Delta T \\ 180(\alpha) &=60 \times 24 \times 10^{-6}+120 \times 30 \times 10^{-6} \\ \alpha &=\frac{24 \times 10^{-6}+60 \times 10^{-6}}{3}=28 \times 10^{-6} /{ }^{\circ} \mathrm{c} \end{aligned}

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Rakesh

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