First slide

Thermal expansion

Question

The ratio of the lengths of two rods is 4:3. The ratio of their coefficients of cubical expansion is 2:3. Then the ratio of their linear expansions when they are heated through same temperature difference is

Moderate

A

2:1
B

1:2
C

8:9
D

9:8

Solution

Given that l₁ : l₂ = 4 : 3
α₁ : α₂ = γ₁ : γ₂= 2 : 3; Δt₁ : Δt₂ = 1 : 1; Δl₁ : Δl₂ = ?
We have $\large \frac {\Delta l}{l \Delta t}\Rightarrow \frac {\alpha_1}{\alpha_2}=\frac {\Delta l_1}{\Delta l_2}\frac {l_2}{l_1}\frac {\Delta t_2}{\Delta t_1}$
$\large \frac {2}{3}=\frac {\Delta l_1}{\Delta l_2}\frac 34\left ( \frac 11 \right )\Rightarrow \frac {\Delta l_1}{\Delta l_2}=\frac 89=8:9$

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