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If two rods of length L and 2L having coefficients of linear expansion $\;\alpha\;$ & $\;2 \alpha\;$ respectively are connected such that length becomes 3L ,The average coefficient of linear expansion of the composite rod equals ---


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Answer : $\;(\large\frac{5}{3})\;\alpha$
Explanation :
$L_{1}=L (1+\alpha \bigtriangleup T)$
$L_{2}=2L (1+2\alpha \bigtriangleup T)$
$=3L + 5 \alpha \bigtriangleup T$
$=3L\; (1+ \large\frac{5}{3} \alpha \bigtriangleup T)$
Therefore , Coefficient of linear expansion of rod =$\;\large\frac{5}{3} \alpha$
answered Mar 15, 2014 by yamini.v

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