Question

On heating a uniform metallic cylinder, length increases by $3\%$. The area of cross - section of its base will increase by

• A. $1.5\%$
• B. $3\%$
• C. $9\%$
• D. $6\%$

Answer 1

The correct option is D $6\%$

The relation between superficial (or areal coefficient) and linear coefficient for a solid object is given by
$\beta =2\alpha$
Given, percentage increase in length for a small change in temperature $(\alpha \times \Delta T)=3\%$
$\therefore$ Percentage increase in area of cross-section for small change in temperature $(\beta \times \Delta T)=2(\alpha \times \Delta T)=2\times 3=6\%$

Thus, Area of cross-section increases by $6\%$.
Hence, option (d) is the correct answer.