Question

A semicircular metal ring subtends at an angle of 180° at the center of a circle. Find out what happens to this angle when it is heated.
A) The angle remains constant.
B) The angle increases slightly.
C) The angle decreases slightly.
D) The angle becomes $360^\circ$

Answer 1

Hint: A metal expands when its temperature increases. The expansion can be a change in its length, its area, or its volume. This is referred to as thermal expansion.

Complete answer:
Based on the concept of thermal expansion find out what happens to the angle.
An increase in the dimensions (length, area, or volume) of an object due to an increase in its temperature is termed as thermal expansion. If there is an increase in the length of the body it is referred to as linear expansion. If there is an increase in the area of the body it is referred to as area expansion and if there is an increase in the volume of the body it is referred to as volume expansion.
Here, the semicircular ring is said to be subtended at an angle of $180^\circ$ at the center of a circle. This ring is then heated. Since the ring is made of metal and as metals are good conductors of heat, the semicircular ring will expand causing the free space inside of the ring to expand too. But, never at any instant of expansion will the angle at which the ring is subtended change.

Therefore, when heated the angle remains constant.

Note:
- If the ends of the semicircular ring were fixed so that it does not undergo thermal expansion on heating, a strain will be developed in it. The corresponding stress in the semicircular ring is called thermal stress.
- Here as the semicircular ring expands, both its inner radius and outer radius expand. It will be as if its entire surface is being stretched out in all directions.