Question

To increase the length of brass rod by $2\%$ its temperature should increase by $(\alpha ={0.00002}^o{C}^{-1})$:

• A. ${800}^{o}C$
• B. ${900}^{o}C$
• C. ${1000}^{o}C$
• D. ${1100}^{o}C$

Answer 1

The correct option is C ${1000}^{o}C$

The change in the length of brass rod is, $\frac{△L}{L}=2\%=\frac{2}{100}$

The coefficient of linear expansion of the rod is $\alpha ={0.00002}^o{C}^{-1}$

The change in temperature can be obtained as:

$\Delta T=\frac{\Delta L}{\alpha L}$

$=\frac{2}{100\times 0.00002}=\frac{1}{0.001}$

$={10}^3={1000}^{o}C$