Question

The coefficient of linear expansion of a metal is $1\times 10^{-5}{/}^{\circ }C$. The percentage increase in area of a square plate of that metal when it is heated through $100^{\circ }C$ is

• A. 0.02%
• B. 0.1%
• C. 0.001%
• D. 0.2%

Answer 1

Answer: (D)

let's assume $L$ is side square plate and $A$ is area at $0^{\circ }C$ and $L^{\prime }$ and $A^{\prime }$ are side length and area at $100^{\circ }C$ now as we now $\begin{array}{l}A=L\times L\\ L^{\prime }=L(1+t\times \alpha )\\ L^{\prime }=L\left(1+100\times 10^{-5}\right)\\ L^{\prime }=L(1.001)\\ A^{\prime }=L^{\prime }\times L^{\prime }\\ A^{\prime }=L(1.001)\times L(1.001)\\ A^{\prime }=A(1.002)\end{array}$ so change in area is $0.2\%$