A sheet of steel is 40 cm long and 5 cm broad at $0^{\circ} \mathrm{C}$. The surface area of the sheet…

A sheet of steel is 40 cm long and 5 cm broad at $0^{\circ} \mathrm{C}$. The surface area of the sheet increases by $1.4 \mathrm{~cm}^2$ at $100^{\circ} \mathrm{C}$. Coefficient of linear expansion of steel is
  1. $1.9 \times 10^{-5} /{ }^{\circ} \mathrm{C}$
  2. $2.4 \times 10^{-5} /^{\circ} \mathrm{C}$
  3. $3.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$
  4. $7 \times 10^{-5} /{ }^{\circ} \mathrm{C}$

Solution

$\begin{aligned} \beta & =\frac{\mathrm{A}_2-\mathrm{A}_1}{\mathrm{~A}_1 \Delta \mathrm{~T}} \\ \therefore \quad \beta & =\frac{1.4}{40 \times 5 \times 100}=\frac{14 \times 10^{-4}}{20}=7 \times 10^{-5} /{ }^{\circ} \mathrm{C} \\ \alpha & =\frac{\beta}{2}=\frac{7 \times 10^{-5}}{2}=3.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}\end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 1)

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