Question

If two quantities (e.g. X and Y) have different dimensions (dimensions in the sense of length, mass, or time), could the product XY ever be physically meaningful?

Obviously X/Y could be, in something like miles/hour. I'm pretty sure that it is possible to multiply quantities with different dimensions, but is the product ever physically meaningful? I just can't imagine something like foot grams, foot hours, or gram hours ever being physically meaningful.

Answer 1

The product of X and Y can be physically meaningful.

For example velocity has dimension or unit 'm/s' and time has unit 's' velocity ×time = displacement (m) which is a physically meaningful quantity.

It is not that every products leads to a meaningful quantity, but not every products are meaningless.

Another example is Q= It unit of Q is As or C.

Maybe there won't be any physical quantity with randomly combined units like foot grams, foot hours etc. But it is not a case of all physical quantities. Sometimes X/Y can also be meaningless.