Question

If two rods of length L and 2L having coefficient of linear expansion a and 2a respectively are connected so that total length becomes 3L, the average coefficient of linear expansion of the composition rods equals –

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

Answer 1

Answer: (C)

$\frac{5}{3}$a

Answer 2

\ a = $\frac{\Delta\mathcal{l}}{L\Delta T}$

for A : a = $\frac{\Delta\mathcal{l}_{1}}{L\Delta T}$ Ž Dl₁ = L a DT

for B : 2a = $\frac{\Delta\mathcal{l}_{2}}{2L\Delta T}$ Ž Dl₂ = 4L a DT

For composition

a_avg. = $\frac{\Delta\mathcal{l}_{1} + \Delta\mathcal{l}_{2}}{3L\Delta T}$ = $\frac{\alpha L\Delta T + 4L\alpha\Delta T}{3L\Delta T}$ = $\frac{5}{3}$ a