Question

When the temperature of a metal wire is increased from $0^{\circ }\text{C}\text{to}{10}^{\circ }\text{C}$, its length increased by $0.02\%$. The percentage change in its mass density will be closest to

• A. $0.06$
• B. $2.3$
• C. $0.008$
• D. $0.8$

Answer 1

The correct option is A $0.06$

Change in length of the metal wire $\left(\Delta l\right)$ when its temperature is changed by $\Delta T$ is given by
$\Delta l=l\alpha \Delta T$
Here, $\alpha$ Coefficient of linear expansion
Here, $\Delta l=0.02$%, $\Delta T={10}^{\circ }\text{C}$
$\therefore \alpha =\frac{\Delta l}{l\Delta T}=\frac{0.02}{100\times 10}\Rightarrow \alpha =2\times {10}^{-5}$

Volume coefficient of expansion, $\gamma =3\alpha =6\times {10}^{-5}$
$\frac{\Delta V}{V}\times 100=\gamma \Delta T=(6\times {10}^{-5}\times 10\times 100)=6\times {10}^{-2}$
Volume increase by $0.06\%$
$\because \rho =\frac{M}{V}$
Therefore, density decrease by $0.06\%$.