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 $0.2 \%$