Question

When the temperature of a copper coin is raised by ${80}^{\circ }\text{C}$, it’s 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 $0.25\times {10}^{–4}{/}^{\circ }\text{C}$

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 $0.25\times {10}^{–4}{/}^{\circ }\text{C}$

$\frac{\Delta A}{A}\times 100=2[\frac{\Delta l}{l}\times 100]$
$\Rightarrow$ % increase in Area $=2\times 0.2=0.4$
Percentage rise in the thickness is 0.2 %
$\frac{\Delta V}{V}\times 100=3\times 0.2=0.6\%$
Since $\Delta l=l\alpha \Delta T$
$\frac{\Delta l}{l}\times 100=\alpha \Delta T\times 100=0.2$
$\Rightarrow \alpha =0.25\times {10}^{-4}{/}^{\circ }\text{C}$