Question

Suppose two quantities, A and B, have different dimensions. Determine which of the following arithmetic operations could be physically meaningful. (Select all that apply.)

B-A A-B A+B AB A/B

Answer 1

Answer: AB, A/B

Explanation:

If two quantities have different dimensionality, there are certain things you can and cannot do.

Addition and subtraction (which is negative addition) - no. So A+B, A-B, etc are forbidden.

So, options B-A A-B A+B are discarded.

As an example, take distance and time. You can't add 10 seconds to 3 metres.

Multiplication and division are fine. Using our example, you can get meters per second (which is speed) and technically you can get meter-seconds, although I can't think what that might be used for. Or consider energy and time. Joules per second is power and Joule-second is the unit for Planck's constant.