A hole is drilled in a metal sheet. At 27 °C, the diameter of hole is 5 cm. When the sheet is heated to 177 °C, the change in the diameter of hole is $$d \times 10^{-3}$$ cm. The value of $$d$$ will be _____$$10^{-3} cm$$, if coefficient of linear expansion of the metal is $$1.6 \times 10^{-5}$$ / °C

A hole of diameter 5 cm in a metal sheet is heated from 27 degrees C to 177 degrees C, and we wish to find the change in diameter. When a metal is heated, all linear dimensions expand uniformly (including holes). The change in a linear dimension is given by $$ \Delta L = L \alpha \Delta T $$ where $$\alpha$$ is the coefficient of linear expansion.

Here, $$D = 5$$ cm, $$\alpha = 1.6 \times 10^{-5}$$ /degrees C, and $$\Delta T = 177 - 27 = 150$$ degrees C. Substituting these values yields $$ \Delta D = 5 \times 1.6 \times 10^{-5} \times 150 = 5 \times 24 \times 10^{-4} = 12 \times 10^{-3}\;\text{cm}$$. Therefore $$d = 12$$. The answer is 12.