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

 

1. AB

2. A/B

3. B-B

4. A-B

5. A+B

 

I have tried choices 123 and 13, yet both were wrong. I know that 4 and 5 are wrong because you are subtracting different units. I thought that 2 was wrong because what if B=0, then it would be undefined. For 3, you are subtracting within the same unit, so it has to be correct. I am not sure at this point. Any advice is welcome.

Because the question talks about whether or not the expressions could be physically meaningful, I think the B=0 case does not exclude 2 as a correct answer. 1, 2, and 3 can all represent physical quantities, while 4 and 5 cannot.

I tried 123 and I was wrong.

Is it some multiple answer test or something? In the broadest sense, all of them could be physically meaningful in the same way complex math is actually used to describe many physical phenomena and consists of a real and imaginary part, comparable to a sum of two different quantities.

I agree but I believe that the quest is saying A is one unit and B is another. So I said lets say A=meters and B=seconds. The first 3 make sense but not the last two.

If B-B was deemed to be not physically meaningful by the test writer, then it would be 1 & 2.

Yes, I'd go with B-B=0 units being meaningful myself, but maybe the test maker doesn't consider 0 units meaningful.

i think only 1