Question

A hole is drilled in a copper sheet. The diameter of the hole is $4.24\text{cm}$ at $27{}^{\circ }\text{C}$. What is the change in the diameter of the hole when the sheet is heated to $227{}^{\circ }\text{C}$ ?
$[\alpha =1.70\times {10}^{-5}/{}^{\circ }\text{C}]$.

• A. $1.44\times {10}^{-2}\text{cm}$
• B. $1.96\times {10}^{-2}\text{cm}$
• C. $1.78\times {10}^{-2}\text{cm}$
• D. $1.28\times {10}^{-2}\text{cm}$

Answer 1

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

Given:
Diameter of the hole, $d=4.24\text{cm}$
Initial temperature, $T_1=27{}^{\circ }\text{C}$
Final temperature, $T_2=227{}^{\circ }\text{C}$
Co-efficient of linear expansion of copper, $\alpha =1.70\times {10}^{-5}/{}^{\circ }\text{C}$.
To find: Change in diameter, $\Delta d=?$
We know that change in linear dimension on heating is given by
$\Delta d=\alpha d\Delta T$
$\Rightarrow \Delta d=1.70\times {10}^{-5}\times 4.24\times (227-27)$
$\Rightarrow \Delta d=1.44\times {10}^{-2}\text{cm}$