Question

A thin copper wire of length L increases in length by 1%, when heated from \(T_1\) to \(T_2\). What is the percentage change in area when a thin copper plate having dimensions \((10L \times 2L)\) is heated from \(T_1\) to \(T_2\)?

• A. 2%
• B. 20%
• C. 10%
• D. 40%

Hint:

Area expansion is approximately twice the linear expansion for small changes.

Answer 1

The Correct Option is A

Concept: Linear expansion: \[ \frac{\Delta L}{L} = \alpha \Delta T \] Area expansion: \[ \frac{\Delta A}{A} = 2\alpha \Delta T \]

Step 1: Given linear expansion.
\[ \frac{\Delta L}{L} = 1\% = 0.01 \Rightarrow \alpha \Delta T = 0.01 \]

Step 2: Area expansion.
\[ \frac{\Delta A}{A} = 2 \times 0.01 = 0.02 = 2\% \]