# 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 ---

$(a)\;1.5\;\alpha\qquad(b)\;(\large\frac{5}{3})\;\alpha\qquad(c)\;1.25\;\alpha\qquad(d)\;(\large\frac{7}{5})\;\alpha$

Answer : $\;(\large\frac{5}{3})\;\alpha$
Explanation :
$L_{1}=L (1+\alpha \bigtriangleup T)$
$L_{2}=2L (1+2\alpha \bigtriangleup T)$
$L_{3}=L_{1}+L_{2}$
$=3L + 5 \alpha \bigtriangleup T$
$=3L\; (1+ \large\frac{5}{3} \alpha \bigtriangleup T)$
Therefore , Coefficient of linear expansion of rod =$\;\large\frac{5}{3} \alpha$