If two rods of length L and 2L having coefficients of linear expansion α and 2α , respectively, are connected such that total length becomes 3L, the average coefficient of linear expansion of the composition rod equals

Question

If two rods of length L and 2L having coefficients of linear expansion α and 2α , respectively, are connected such that total length becomes 3L, the average coefficient of linear expansion of the composition rod equals (A) (3/2)α  (B) (5/2)α  (C) (5/3)α  (D) none of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-ttbtd56jronezlhi.jpg" /> Δ l=Δ l1+Δ l2 α e q3LΔ T=α LΔ T+2α × 2LΔ T 3α e q=5α ⇒ α e q=(5/3)α

Q. If two rods of length $L$ and $2 L$ having coefficients of linear expansion $α$ and $2 α$ , respectively, are connected such that total length becomes $3 L,$ the average coefficient of linear expansion of the composition rod equals

$\frac{3}{2} α$

$\frac{5}{2} α$

$\frac{5}{3} α$

none of these

$Δ l = Δ l_{1} + Δ l_{2}$
$α_{e q} 3 L Δ T = αL Δ T + 2 α \times 2 L Δ T$
$3 α_{e q} = 5 α$
$\Rightarrow α_{e q} = \frac{5}{3} α$

Q. If two rods of length L and 2L having coefficients of linear expansion α and 2α , respectively, are connected such that total length becomes 3L, the average coefficient of linear expansion of the composition rod equals

23​α

25​α

35​α