Question

If two rods of length $L$ and $2L$ having coefficients of linear expansion $\alpha$ and $2\alpha$ respectively are connected so that total length becomes $3L$, the average coefficient of linear expansion of the composition rod equals:

• A. $\frac{3}{2}\alpha$
• B. $\frac{5}{2}\alpha$
• C. $\frac{5}{3}\alpha$
• D. None of these

Answer 1

The correct option is C $\frac{5}{3}\alpha$

$\begin{array}{c}{L}_1=L\left(1+\alpha \Delta T\right)\\ L_2=2L\left(1+2\alpha \Delta T\right)\\ L_3=L_1+L_2\\ =3L+5\alpha \Delta T\\ =3L\left(1+\frac{5}{3}\alpha \Delta T\right)\\ Therefore,coefficientoflinearansionofrod=\frac{5}{3}\alpha \end{array}$

Hence,

option $\left(C\right)$ is correct answer.