Question

A hole is drilled in a copper sheet. The diameter of the hole is 4.24cm at ${27.0}^{o}C$. what is the change in the diameter of the hole when the sheet is heated to ${227}^{o}C$ ?
$\alpha$ for copper = $1.70\times {10}^{-5}{K}^{-1}$

• A. $1.44\times {10}^{-2}cm$
• B. $14.4\times {10}^{-2}cm$
• C. $144\times {10}^{-2}cm$
• D. $0.144\times {10}^{-2}cm$

Answer 1

The correct option is A $1.44\times {10}^{-2}cm$

As on increasing temperature,

thermal expansion will be uniform throughout the sheet. So,

$\Delta d=\left(d\right)\left(\alpha \right)\Delta T$

Here $\Delta d=\left(4.24cm\right)(1.7\times {10}^{-5})(227-27)$

$\Delta d=\left(4.24\right)\left(1.7\right)\left(200\right)\times {10}^{-5}$cm

$\Delta d=1.4416\times {10}^{-2}$cm

Option A is correct.