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A bimetallic strip is formed out of two identical strips, one of copper and other of brass. The coefficients of linear expansion of the two metals are $a_{C}$ and $a_{B}$ On heating the temperature of the strip goes up by $Δ T$ and the strip bends to form an arc of radius of curvature R. Then R is

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directly proportional to $Δ T$

proportional to $|a_{B} - a_{c}|$

inversely proportional to $|a_{B} - a_{c}|$

independent of $Δ T$

answer is D.

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Detailed Solution

Let $L_{0}$ be the initial length of each strip before heating.Length after heating will be

$L_{B} = L_{0} (1 + α_{B} Δ T) = (R + d) θ$

$L_{C} = L_{0} (1 + α_{C} Δ T) = R θ \Rightarrow \frac{R + d}{R} = \frac{1 + α_{B} Δ T}{1 + α_{C} Δ T}$

$\Rightarrow 1 + \frac{d}{R} = 1 + (α_{B} - α_{C}) Δ T$

$\Rightarrow R = \frac{d}{(α_{B} - α_{C}) Δ T} \Rightarrow R \propto \frac{1}{Δ T}$

$and R \propto \frac{1}{(α_{B} - α_{C})}$

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