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

Initial length of combination is $L+2L=3L$

Increment in first rod is $L\alpha \Delta t$

Increment in second rod is $\left(2L\right)\left(2\alpha \right)\Delta t=4L\alpha \Delta t$

So increment in combination is sum of both so $5L\alpha \Delta t$

Initial length of combination was $3L$ so coefficient for combination is $\frac{change}{\text{initial length* change in temperature}}$

$=\frac{5L\alpha \Delta t}{3L\Delta t}=5\alpha /3$

Option C is correct.