Question

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

• A. 4.945 cm
• B. 5.045 cm
• C. 5.001 cm
• D. 5.450 cm

Answer 1

The correct option is B

5.045 cm

Let $L_0$ be the initial diameter of metal disc, $\alpha$ be the coefficient of linear expansion of metal and $t$ be the change in temperature.
Given, $L_0=5cm$, $\alpha =1.8\times {10}^{-5}{}^{\circ }C$ and $t=500{}^{\circ }C$
Final diameter, $L_t=L_0(1+(\alpha \times t\left)\right)$ $L_t=5\times [1+((1.8\times {10}^{-5})\times 500\left)\right]=5.045cm$