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

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

Let diameter be ${d}_{0}$ at $27 ° C$ and ${d}^{'}$ at $177 ° C$. Therefore, we can write

${d}^{'} = {d}_{0}\left(1 + \alpha\DeltaT\right)$

Therefore, change in diameter will be

$⇒ {d}^{'} - {d}_{0} = \left(5\right) \times \left(1 . 6 \times {10}^{- 5}\right) \times \left(177 - 27\right)$

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

Hence, required value of $d = 12$.