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

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2 : 1

1 : 2

8 : 9

9 : 8

answer is C.

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Detailed Solution

Given that l₁ : l₂ = 4 : 3
$α_{1} : α_{2} = γ_{1} : γ_{2} = 2 : 3, ∆ t_{1} : ∆ t_{2} = 1 : 1 ∆ l_{1} : ∆ l_{2} = ?$
we have
$α = \frac{∆ l}{l ∆ t} \Rightarrow \frac{α_{1}}{α_{2}} = \frac{∆ l_{1}}{∆ l_{2}} \frac{l_{2}}{l_{1}} \frac{∆ t_{2}}{∆ t_{1}} \frac{2}{3} = \frac{∆ l_{1}}{∆ l_{2}} \frac{3}{4} (\frac{1}{1}) \Rightarrow \frac{∆ l_{1}}{∆ l_{2}} = \frac{8}{9} = 8 : 9$

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