Q137 / 160 · TS EAMCET 2020 (11 Sep Shift 2) · Physics
A sheet of steel at $20^{\circ} \mathrm{C}$ has size as shown in figure below. If the co-efficient of linear expansion for steel is $10^{-5 \circ} \mathrm{C}^{-1}$, then what is the change in the area at $60^{\circ} \mathrm{C}$ ?
- A$0.84 \mathrm{~cm}^2$
- Correct answerB$0.64 \mathrm{~cm}^2$
- C$0.24 \mathrm{~cm}^2$
- D$0.14 \mathrm{~cm}^2$
Solution
Given, $t_1=20^{\circ} \mathrm{C}$ and $t_2=60^{\circ} \mathrm{C}$
Coefficient of linear expansion,
$\alpha=10^{-5 \circ} \mathrm{C}^{-1}$
As we know that, coefficient of area expansion is
$\beta=\frac{\Delta A}{A \times \Delta T} \Rightarrow 2 \alpha=\frac{\Delta A}{A \times \Delta T} \quad[\because \beta=2 \alpha]$
$\Delta A=2 \alpha \times A \times \Delta T$
$=2 \times 10^{-5} \times 40 \times 20 \times 10^{-4} \times(60-20)$
$=0.64 \times 10^{-4} \mathrm{~m}^2=0.64 \mathrm{~cm}^2$
Hence, the correct answer is option: 'B'.