Two rods, one of copper ( Cu) and the other of iron ( Fe) having initial lengths L₁ and L₂ respectively are connected together to form a single rod of length L₁ + L₂. The coefficient of linear expansion of Cu and Fe are αc and αi respectively. If the length of each rod increases by the same amount when their temperatures are raised by t°C, then ratio of (L₁ - L₂)/(L₁ + L₂) will be (a) (αi)/(αc + αi) (b) (αc)/(αc + αi) (c) (αi - αc)/(αc + αi) (d) (αc - αi)/(αc + αi)

Answer: (c). Equal expansion: L₁αc = L₂αi ⇒ (L₁)/(L₂) = (αi)/(αc). (L₁ - L₂)/(L₁ + L₂) = (αi - αc)/(αi + αc) So the answer is (c).

Two rods, one of copper ( Cu) and the other of iron ( Fe) having… | MHT CET 2024 (3 May, Shift 2)

Q30MHT CET 2024 · 3 MAY · SHIFT 2Difficult

Thermometry & Thermal Expansion

Two rods, one of copper ( Cu $)$ and the other of iron ( Fe) having initial lengths $L_1$ and $L_2$ respectively are connected together to form a single rod of length $L_1 + L_2$ . The coefficient of linear expansion of Cu and Fe are $\alpha_c$ and $\alpha_i$ respectively. If the length of each rod increases by the same amount when their temperatures are raised by $t^{\circ}\text{C}$ , then ratio of $\frac{L_1 - L_2}{L_1 + L_2}$ will be

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Answer: (c)

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

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Thermometry & Thermal Expansion question from MHT CET 2024 (3 May, Shift 2)

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