Question

The diameter of a metal ring is $D$ and the coefficient of linear expansion is $\alpha$. If the temperature of the ring is increased by $1^0C$, the circumference and the area of the ring will increase by

• A. $\pi\,D \alpha ,2\pi\,D\alpha$
• B. $2\pi\,D \alpha ,2\pi\,D^2\alpha$
• C. $\pi\,D\alpha,\frac{\pi\,D\alpha}{2}$
• D. $\pi\,D\alpha,\frac{\pi\,D^2\alpha}{2}$

Answer 1

Answer: (D)

Increase in Diameter, $\Delta D = D \alpha$
So, increase in circumference $=\pi \Delta D =\pi D \alpha$
Also, we note that coefficient of area expansion $=2 \alpha$
So change in area $=$ initial area $\times 2 \times \alpha=\frac{\pi D ^{2}}{4} \times 2 \times \alpha=\frac{\pi D ^{2} \alpha}{2}$