Question

A circular metal disc of diameter $5\text{cm}$ is heated by $500{}^{\circ }\text{C}$. If the coefficient of linear expansion of the metal is $1.8\times {10}^{-5}{}^{\circ }{\text{C}}^{-1}$, what will be its final diameter?

• A. $4.945\text{cm}$
• B. $5.045\text{cm}$
• C. $5.450\text{cm}$
• D. $5.001\text{cm}$

Answer 1

The correct option is B $5.045\text{cm}$

Let ${\text{L}}_{\circ }$ be the initial diameter of metal disc, $\alpha$ be the coefficient of linear expansion of the metal and $\Delta \text{T}$ be the change in temperature.

Given, ${\text{L}}_{\circ }=5\text{cm}$, $\alpha =1.8\times {10}^{-5}{}^{\circ }\text{C}$ and $\Delta \text{T}=500{}^{\circ }\text{C}$

Final diameter, ${\text{L}}_t={\text{L}}_{\circ }(1+(\alpha \times \Delta \text{T}\left)\right)$

${\text{L}}_t=5\times [1+((1.8\times {10}^{-5})\times 500\left)\right]$

$=5.045\text{cm}$