Video Transcript
Quantity π has dimensions of πΌ times π squared. Quantity π has dimensions π to the negative two times π to the negative one. What are the dimensions of π times π?
We can symbolize the dimensions of π like this. They are πΌ, thatβs current, times π, thatβs time, squared. Similarly, the dimensions of π are π, time, to the negative two times π, mass, to the negative one. We want to solve here for the dimensions of π times π. This is equal to the dimensions of π times the dimensions of π. Thatβs equal to current times time squared multiplied by time to the negative two times mass to the negative one. When we multiply π squared by π to the negative two, the result of that is one, leaving us with dimensions of current πΌ times mass π to the negative one. The dimensions of π times π equal πΌ times π to the negative one.