A hole is drilled in a metal sheet. At 27   ° C , the diameter of hole is 5   cm . When the…

Expansion of hole will be similar to that of an imaginary disc.

Let diameter be $d_0$ at $27 °\mathrm{C}$ and $d^{\text{'}}$ at $177 °\mathrm{C}$. Therefore, we can write

$d^{\text{'}}=d_0\left(1+\alpha \Delta T\right)$

Therefore, change in diameter will be

$\Rightarrow d^{\text{'}}-d_0=\left(5\right)\times \left(1.6\times {10}^{-5}\right)\times \left(177-27\right)$

$=12\times {10}^{-3} \mathrm{cm}$

Hence, required value of $d=12$.