Question

The coefficient of linear expansion of a rod is $\alpha$ and its length is $L$. The increase in temperature required to increases its length by $1\%$ is :

• A. $\frac{1}{\alpha }$
• B. $\frac{1}{10\alpha }$
• C. $\frac{1}{50\alpha }$
• D. $\frac{1}{100\alpha }$

Answer 1

Answer: (D)

$\frac{1}{100\alpha }$

Given,

Coefficient of linear expansion=$\alpha$

$\frac{\Delta L}{L}=\frac{1}{100}$

We know,

$\Delta L=L\alpha \Delta T$

$\frac{\delta L}{L}=\alpha \Delta T=\frac{1}{100}$

$\Delta T=\frac{1}{100\alpha }$

Option $\text{D}$ is the correct answer.