Question

A metal sheet with a circular hole is heated. The hole
a) gets larger.
b) gets smaller.
c) remains of the same size.
d) gets deformed

Answer 1

Hint: Whenever a sheet is heated it undergoes superficial expansion, i.e. its surface area increases to some extent. The expansion is seen along the edges of the sheet as they are free to expand on heating. Hence from this result we can easily predict the consequences of heating on the hole.

Formula used:
$U=-\dfrac{GMm}{r}$
$K=\dfrac{1}{2}m{{v}_{0}}^{2}$

Complete step by step answer:
To begin with, let us discuss the causes of expansion.
All solids consist of atoms and molecules. At any given temperature, these atoms and molecules are held at equilibrium distance by the force of attraction. When solid is heated, the amplitude of vibration of its atoms and molecules increase which results in decrease of the force of attraction between the particles. This results in thermal expansion of the solid.
Given below is a diagram of a circular sheet, where the radius of the hole in the sheet is r and the outer radius of the sheet is R.

As the sheet undergoes expansion its outer radius will increase. Since the sheet is very thin the area occupied by the sheet will somewhat be the constant. Hence we can conclude that the sheet along its edges will expand radially outwards and hence the hole in the sheet will be larger.

Note:
The sheet is assumed to be having not much thickness. Hence we can conclude that the sheet won't radially expand in wards. If the thickness of the sheet is sufficiently larger, then the sheet will expand in both the directions.