Chapter 6, Problem 35A

What is the difference between saying that one quantity is proportional to another and saying it is equal to another?

To determine

The difference between saying that one quantity is proportional to another and saying it is equal to another.

Explanation of Solution

Introduction:

In physics, many times it came across the terminology proportional, equal. The use of these terminologies depends on the situation.

When it is say that the two quantities are in proportional to each other, then these two values connected with each other by multiplication or division. Their product or ratio gives the constant value and this constant is known as proportionality constant.

Depending the how these two values connected with the constant there are two different types of proportionality:

1. Directly proportional
2. Inversely proportional.

In proportional, change in one quantity implies that corresponding change in the other quantity by the same rate. In this case two quantities may not have the same unit. When one quantity increases or decrease, correspondingly another quantity increases or decreases with same rate. In this case, two quantities are not necessarily ideal.

Another way describe the relation between two quantity is the by means of equality. When it is said that the two quantities are said to be equal, then their value should be equal. There will be no change in the values of quantities. Normally we equate the quantity whose unit is same.

Conclusion:

Therefore, if the two quantities are proportional, the change in one quantity implies that there will be change in another quantity, whereas if two quantities are equal, this implies that the quantities are identical.