Question Video: Determining the Overall Dimensions of One Quantity Divided by Another | Nagwa Question Video: Determining the Overall Dimensions of One Quantity Divided by Another | Nagwa

# Question Video: Determining the Overall Dimensions of One Quantity Divided by Another Physics • First Year of Secondary School

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Quantity π has dimensions of πΌ. Quantity π has dimensions of πΌπβ»ΒΉ. What are the dimensions of π/π?

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### Video Transcript

Quantity π has dimensions of πΌ. Quantity π has dimensions of πΌ times π to the negative one. What are the dimensions of π divided by π?

Here, weβre told that the dimension of quantity π is πΌ. We can assume that πΌ represents current. Quantity π has dimensions πΌ times π to the negative one. Here, π we can assume is time. If we calculate π divided by π, we want to know the dimensions of that fraction. This will be equal to the dimensions of π divided by the dimensions of π. Thatβs equal to πΌ divided by πΌ times π to the negative one.

Note that since we have dimensions of πΌ in both numerator and denominator, these dimensions cancel out. All that remains is one over π to the negative one. If we multiply both numerator and denominator of this fraction by π, then in the denominator, π times one over π becomes one. So the fraction simplifies to time π. The dimensions of π divided by π are π.

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