Physical quantities which do not depend upon other quantities for their complete definition are known as fundamental or base quantities. e.g. length, mass, time, temperature, electric current, amount of substance, and luminous intensity, etc.

Derived quantities

Physical quantities that can be expressed as combinations of base (fundamental) quantities are known as derived quantities. e.g. Speed, volume, velocity, acceleration, force, pressure, momentum, energy, etc.

Units of physical quantities

The chosen reference standard of measurement in multiples of which, a physical quantity is expressed is called the unit of that quantity. e.g. \(\text { Physical Quantity }=\text { Numerical Value } \times \text { Unit }\)

System of Units

\(\begin{array}{|c|c|c|c|c|c|}
\hline & \text { MKS } & \text { CGS } & \text { FPS } & \text { MKSQ } & \text { MKSA } \\
\hline \text { (i) } & \begin{array}{c}
\text { Length } \\
(\mathrm{m})
\end{array} & \begin{array}{c}
\text { Length } \\
(\mathrm{cm})
\end{array} & \begin{array}{c}
\text { Length } \\
(\mathrm{ft})
\end{array} & \begin{array}{c}
\text { Length } \\
(\mathrm{m})
\end{array} & \begin{array}{c}
\text { Length } \\
(\mathrm{m})
\end{array} \\
\hline \text { (ii) } & \begin{array}{c}
\text { Mass } \\
(\mathrm{kg})
\end{array} & \begin{array}{c}
\text { Mass } \\
(\mathrm{g})
\end{array} & \begin{array}{c}
\text { Mass } \\
(\text { pound })
\end{array} & \begin{array}{c}
\text { Mass } \\
(\mathrm{kg})
\end{array} & \begin{array}{c}
\text { Mass } \\
(\mathrm{kg})
\end{array} \\
\hline \text { (iii) } & \begin{array}{c}
\text { Time } \\
(\mathrm{s})
\end{array} & \begin{array}{c}
\text { Time } \\
(\mathrm{s})
\end{array} & \begin{array}{c}
\text { Time } \\
(\mathrm{s})
\end{array} & \begin{array}{c}
\text { Time } \\
(\mathrm{s})
\end{array} & \begin{array}{c}
\text { Time } \\
(\mathrm{s})
\end{array} \\
\hline \text { (iv) } & – & – & – & \begin{array}{c}
\text { Charge } \\
(\mathrm{Q})
\end{array} & \begin{array}{c}
\text { Current } \\
(\mathrm{A})
\end{array} \\
\hline
\end{array}\)

Fundamental Quantities in S.I. Systems and their Units

\(\begin{array}{|c|l|c|c|}
\hline \text { S.N. } & {\text { Physical Qty. }} & \text { Name of Unit } & \text { Symbol } \\
\hline 1 & \text { Mass } & \text { kilogram } & \mathrm{kg} \\
\hline 2 & \text { Length } & \text { meter } & \mathrm{m} \\
\hline 3 & \text { Time } & \text { second } & \mathrm{s} \\
\hline 4 & \text { Temperature } & \text { kelvin } & \mathrm{K} \\
\hline 5 & \text { Luminous intensity } & \text { candela } & \mathrm{Cd} \\
\hline 6 & \text { Electric current } & \text { ampere } & \mathrm{A} \\
\hline 7 & \text { Amount of substance } & \text { mole } & \text { mol } \\
\hline
\end{array}\)

SI Base Quantities and Units

Supplementary Units

Radian (rad) – for measurement of plane angle
Steradian (sr) – for measurement of solid angle

Dimensional Formula

The relation which express physical quantities in terms of appropriate powers of fundamental units.

Use of dimensional analysis

To check the dimensional correctness of a given physical relation.
To derive the relationship between different physical quantities.
To convert units of a physical quantity from one system to another.

\(
n_{1} u_{1}=n_{2} u_{2} \Rightarrow n_{2}=n_{1}\left(\frac{M_{1}}{M_{2}}\right)^{a}\left(\frac{L_{1}}{L_{2}}\right)^{b}\left(\frac{T_{1}}{T_{2}}\right)^{c}
\)
where \(\mathrm{u}=\mathrm{M}^{\mathrm{a}} \mathrm{L}^{\mathrm{b}} \mathrm{T}^{\mathrm{c}}\)

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