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Question Video: Finding the Dimensions of a Quantity Measured in Kilograms per Square Meter Physics • First Year of Secondary School

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What are the dimensions of a quantity that can be measured in units of kg⋅m²?

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Video Transcript

What are the dimensions of a quantity that can be measured in units of kilograms times meters squared?

In this question, we’re given a set of units, and we want to convert them in a sense into dimensions. We see then that dimensions and units are not the same. A unit, such as a kilogram or a meter, is a particular way of expressing a physical quantity. A dimension, on the other hand, is that quantity itself, such as length or time or current. In this compound unit, we see two individual units. The kilogram is the SI base unit for mass, and the meter is the SI base unit for length.

Mass and length are physical quantities that can be measured in units of kilograms and meters. Mass and length then are dimensions. We represent the dimension of mass using a capital M and the dimension of length using a capital L. Therefore, if we convert the units of kilograms meters squared into dimensions, we would get mass times length squared. We can also write this a bit more compactly, and we have then our answer. A quantity that is measured in units of kilograms meters squared has dimensions of mass times length squared.

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