Question

Why are dimensions are required to specify a physical quantity

Answer 1

Heya !!


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A dimensionful physical quantity must have a unit specified in order for it to have a numerical value assigned to it. But, as long as one is not assigning numerical values to it, one need not select a unit.

A dimension is a general type of measurable physical property, such as length, time, or mass. A unit is a standardized way to assign a numerical quantity to properties of a particular dimension. For example, the meter, second, and kilogram are particular units that allow us to assign numbers to measurements of length, time, and mass dimensions.

If by physical quantity one means a physical property that has a dimension, then one can meaningfully speak about such a property without necessarily selecting any particular unit. For example, we can meaningfully talk about someone growing taller or getting heavier without the need to specify particular units of length or mass. Their height and weight (physical quantities) have dimensions, but we’re not forced to specify units unless we make a measurement or assign numerical values to their height and weight.


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Thanks !!

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Answer 2

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The dimension of a physical quantitycan be expressed as a product of the basic physical dimensions such aslength, mass and time, each raised to a rational power. The dimension of aphysical quantity is more fundamental than some scale unit used to express the amount of that physical quantity.


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