Question

A rectangular metal plate having length $1.2\text{m}$ and breadth $0.8\text{m}$ is heated from ${10}^{\circ }\text{C}$ to ${110}^{\circ }\text{C}$. Then, choose the correct option(s) :
[Given, coefficient of linear expansion of metal $\alpha =1.5\times {10}^{-5}{/}^{\circ }\text{C}$]

• A. The change in breadth of the rectangular plate is $1.2\times {10}^{-3}\text{m}$.
• B. The change in area of the rectangular plate is $1.2{\text{m}}^2$.
• C. The change in length of the rectangular plate is $1.8\times {10}^{-3}\text{m}$.
• D. The change in area of the rectangular plate is $2.88\times {10}^{-3}{\text{m}}^2$.

Answer 1

Answer: (A), (C), (D)

The change in area of the rectangular plate is $2.88\times {10}^{-3}{\text{m}}^2$.

Given, coefficient of the linear exapnasion $\left(\alpha \right)=1.5\times {10}^{-5}{/}^{\circ }\text{C}$
Then, coefficient of the areal expansion $\left(\beta \right)=2\times 1.5\times {10}^{-5}{/}^{\circ }\text{C}$
$=3\times {10}^{-5}{/}^{\circ }\text{C}$
From the definition of linear expansion, we can say that
Change in length of the plate $\Delta L=L\alpha \Delta T$
From the data given in the question,
$\Delta L=1.2\times 1.5\times {10}^{-5}\times (110-10)=1.8\times {10}^{-3}\text{m}$
Similarly,
Change in breadth of the plate $\Delta B=B\alpha \Delta T$
$\Delta B=0.8\times 1.5\times {10}^{-5}\times (110-10)=1.2\times {10}^{-3}\text{m}$
From the definition of areal expansion, we can say that
Change in area of the plate $\Delta A=A\beta \Delta T$
$\Delta A=(1.2\times 0.8)\times 3\times {10}^{-5}\times (110-10)=2.88\times {10}^{-3}{\text{m}}^2$
Hence options (a) , (c) and (d) are correct.