Question

A hole of 4 cm in diameter is made in a brass plate at a temperature of ${20}^{\circ }C$. The diameter of the hole when the temperature of plate is increased to ${100}^{\circ }C$ is :
$(\alpha =20\times {10}^{-6}{/}^{\circ }C)$

• A. 4.64 cm
• B. 4.064 cm
• C. 4.00064 cm
• D. 4.0064 cm

Answer 1

Answer: (D)

4.0064 cm

Let $d_2$ will be the diameter of the hole.
So $d_2=d_1(1+\alpha dt),$
where $d_1=$ current diameter and $dt=$ change in temperature.
Here, $d_1=0.04$ m, dt $={80}^{\circ }$C and $\alpha =20\times {10}^{-6}{/}^{\circ }C$
Putting these values, we get, $d_2=0.040064$ m $=4.0064$cm