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

The correct option is D 0.2%

let's assume L is side square plate and A is area at 0℃

and L' and A' are side length and area at 100℃

now as we now

$A=L\times L{L}^{\prime }=L(1+t\times \alpha )L^{\prime }=L(1+100\times {10}^{-5})L^{\prime }=L\left(1.001\right)$

$A^{\prime }=L^{\prime }\times L^{\prime }{A}^{\prime }=L\left(1.001\right)\times L\left(1.001\right)A^{\prime }=A\left(1.002\right)$

so change in area is $0.2$