# can we tell the unit of a physical quantity from its dimensions? explain

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### 1 Answer

The short answer of your question is YES. The explanation follows.

In physics any physical quantity can be expressed in terms of basic dimensions (each raised to a certain power). The basic dimensions that, in a certain way of speaking, are postulated are: Length (L), Mass (M), Time (T), absolute temperature (`Theta` ) and electric charge (Q).

The measuring units for these basic dimensions are:

L - meter m

M - kilogram kg

T - second s

`Theta` - Kelvin degree K

Q - Coulomb C

Starting from these basic dimensions and using the laws of physics (the physical definitions of the other physical quantities) one can construct the relation between any physical unit and the basic dimensions.

For example by DEFINITION (second law of physics) force is

F= m*a = m*v/t = m*(d/t)/t

The unit to measure force is the International System (SI) is Newton (N). Therefore

1 N =<F>= <m>*<d>/<t>^2 = M*L/T^2 = 1 kg*m/(s^2)

where the parentheses <> specifies the basic measuring unit for that particular physical quantity.

Therefore it is equivalent say the magnitude of the force is 1 N or 1 kg*m/(s^2).

This is what is called in physics Dimensional Analysis and is a powerful tool because knowing the relation between basic dimensions and a certain physical quantity you can deduce (by reverse reasoning) the physical law that defines that particular quantity.

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