Question

When the temperature of a copper coin is raised by ${80}^{\circ }C$, its diameter increases by 0.2%.

• A. Percentage rise in the area of a face is $0.4\%$
• B. Percentage rise in the thickness is $0.4\%$
• C. Percentage rise in the volume is $0.6\%$
• D. Coefficient of linear expansion of copper is $0.25\times {10}^{-4}{}^{\circ }{C}^{-1}$

Answer 1

Answer: (A), (C), (D)

The correct options are
A Percentage rise in the area of a face is $0.4\%$
C Percentage rise in the volume is $0.6\%$
D Coefficient of linear expansion of copper is $0.25\times {10}^{-4}{}^{\circ }{C}^{-1}$

Since, $Areaexpansion=2\times linearexpansion$
$Volumeexpansion=3\times linearexpansion$
Therefore, area increases by 0.4 % and volume increases by 0.6%
Now $\Delta D/D=0.002=\alpha \Delta \theta$
Therefore $\alpha =0.002/80$
$\alpha =20/80\times {10}^{-4}$
$\alpha =0.25\times {10}^{-4}$
option (A),(C) and (D) are correct