Question

A copper disc has a circular hole at its centre. When the copper disc is heated to raise its temperature, the diameter of the hole will
A. Decrease
B. Not be affected
C. Increase
D. None of these

Answer 1

Hint: Use the formula for the linear thermal expansion of the material.
Also check whether the linear thermal expansion coefficient of the given material is positive or negative.
Copper is anisotropic, its size of the disc as well as the hole increases.

Formula used:
The expression for the linear thermal expansion of a solid material is
\[\Delta L = \alpha {L_0}\Delta T\] …… (1)
Here, \[\Delta L\] is the change in the length of the solid material, \[\alpha \] is the linear thermal expansion coefficient, \[L\] is the original length of the material and \[\Delta T\] is the change in the temperature.

Complete step by step answer:
The copper has a positive thermal expansion coefficient. Hence, the size of the hole in the copper disc will increase and not decrease.
Hence, the option A is incorrect.
The thermal expansion coefficient of copper is not zero. Hence, the size of the hole will not remain the same.
Hence, option B is incorrect.
The size of the hole of the disc increases due to heating.
 Hence, the option D is incorrect.
From equation (1), the change in length of the material is proportional to linear thermal expansion coefficient.
When a metal is heated to increase its temperature, it undergoes expansion.
When heated, the size of the materials having positive thermal expansion coefficient increases.
In the present example, the disc of copper is heated to increase its temperature.
The copper has a positive thermal expansion coefficient. Hence, the size of the hole in the copper disc will increase.
When the temperature of the copper disc is increased, the diameter length of the copper disc increases due to the linear thermal expansion of the diameter.
Since the hole made at the centre of the disc is also circular and made of the same copper metal, it will also undergo linear thermal expansion and its size will increase.

So, the correct answer is “Option C”.

Note:
For the isotropic materials, the expansion of the material is uniform in all directions and for anisotropic materials; the expansion of the material is non-uniform in all directions. Since copper is anisotropic, its size of the disc as well as the hole increases but not uniformly i.e. the size of the hole will increase differently in different directions.