Chapter 21, Problem 43A

A metal ball is just able to pass through a metal ring. When the ball is heated, thermal expansion will not allow it to pass through the ring. What would happen if the ring, rather than the ball, were heated? Would the ball pass through the heated ring? Does the size of the hole in the ring increase, decrease, or stay the same?

To determine

When a metal ring is heated, whether its diameter would be increased or decreased.

Explanation of Solution

Introduction:

When a metal heated, the expansion will take place radially outward.

The thermal expansion of any material can be calculated with the following equation

  $\begin{array}{l}\Delta L={\alpha }_{L}L\Delta T\\ \text{Where,}\\ \Delta L=\text{change in dimensions of object}\\ {\alpha }_L=\text{Linear thermal expansion coefficient}\\ L=\text{actual demensions of the object}\\ \Delta T=\text{change in temperature}\end{array}$

It is clear form this, the metal will expand upon heating.

In this given problem, as the metal ring is heated, its inner diameter will expand according to the above equation.

When the inner diameter expands, the metal ball will pass through the metal ring.

Conclusion:

When the metal ring is heated, it’s hole will increase and therefore the metal ball will pass through the metal ring.