Question

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

• 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 $0.25\times {10}^{-4}{/}^{\circ }C$

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

Increase in diameter due to thermal expansion
$\Delta d=d_0\alpha \Delta t$
$\Rightarrow \frac{\Delta d}{d_0}=\alpha \Delta t$
Percentage increase in diameter
$\frac{\Delta d}{d_0}\times 100=\alpha \Delta t\times 100=0.2$ (given)
$\Rightarrow \alpha =\frac{0.2}{80\times 100}$
$\alpha =0.25\times {10}^{-4}{}^{\circ }{C}^{-1}$
Percentage increase in area
$\frac{\Delta A}{A}\times 100=\beta \Delta t\times 100$
$\frac{\Delta A}{A}\times 100=2\alpha \Delta t\times 100(\because \beta =2\alpha )$
$\frac{\Delta A}{A}\times 100=0.4\%$

Percentage increase in thickness $\left(y\right):$ (It is also a length dimensionally)
$\frac{\Delta y}{y}\times 100=\alpha \Delta t\times 100=0.2\%$
Percentage increase in volume (V)
$\frac{\Delta V}{V}\times 100=\gamma \Delta t\times 100$
$\frac{\Delta V}{V}\times 100=3\alpha \Delta t\times 100$
$\frac{\Delta V}{V}\times 100=0.6\%$