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

Question

If two rods of length L and 2 L having coefficients of linear expansion α and 2 α respectively are connected so that total length becomes 3 L, 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

Δ L =Δ L 1+Δ L 2 α textmix(3 L ) Δ T = L α Δ T +2 L (2 α) Δ T α text mix =(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 so 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

$Δ L = Δ L_{1} + Δ L_{2}$
$α_{mix} (3 L) Δ T = Lα Δ T + 2 L (2 α) Δ T$
$α_{mix} = \frac{5}{3} α$

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

23​α

25​α

35​α