Two rods, one of aluminium and the other of steel, having initial lengths ' L₁ ' and ' L₂ ' are connected together to form a single rod of length (L₁ + L₂). The coefficients of linear expansion of aluminium and steel are ' α₁ ' and ' α₂ ' respectively. If the length of each rod increases by the same amount, when their temperatures are raised by t°C, then the ratio (L₁)/(L₁ + L₂) will be (a) (α₂)/(α₁) (b) (α₁)/(α₂) (c) (α₂)/(α₁ + α₂) (d) (α₁)/(α₁ - α₂)

Answer: (c). Equal expansion: L₁α₁ = L₂α₂ ⇒ (L₁)/(L₂) = (α₂)/(α₁). (L₁)/(L₁ + L₂) = (α₂)/(α₁ + α₂) So the answer is (c).

Two rods, one of aluminium and the other of steel, having initial… | MHT CET 2024 (3 May, Shift 1)

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Thermometry & Thermal Expansion

Two rods, one of aluminium and the other of steel, having initial lengths ' $L_1$ ' and ' $L_2$ ' are connected together to form a single rod of length $(L_1 + L_2)$ . The coefficients of linear expansion of aluminium and steel are ' $\alpha_1$ ' and ' $\alpha_2$ ' respectively. If the length of each rod increases by the same amount, when their temperatures are raised by $t^{\circ}\text{C}$ , then the ratio $\frac{L_1}{L_1 + L_2}$ will be

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Answer: (c)

Equal expansion: $L_1\alpha_1 = L_2\alpha_2 \Rightarrow \dfrac{L_1}{L_2} = \dfrac{\alpha_2}{\alpha_1}$ .
$\dfrac{L_1}{L_1 + L_2} = \dfrac{\alpha_2}{\alpha_1 + \alpha_2}$
So the answer is (c).

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Thermometry & Thermal Expansion question from MHT CET 2024 (3 May, Shift 1)

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