What do you understand by the term derived unit? Give three examp… - Vidyadip

Question

What do you understand by the term derived unit? Give three examples.

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Answer

Derived units. "Derived units are those which can be expressed in terms of fundamental units."
Example.
$
\begin{aligned}
\text { 1. Force } & =\text { mass } \times \text { acceleration } \\
& =\text { mass } \times \frac{\text { velocity }}{\text { time }} \\
& =\text { mass } \times \frac{\frac{\text { distance }}{\text { time }}}{\text { time }}=\frac{\text { mass } \times \text { distance }}{(\text { time })^2} \\
\therefore \text { Force } & =\frac{\text { mass } \times \text { length }}{(\text { time })^2}
\end{aligned}
$
2. S.I. unit of area i.e. $m ^2$ is a derived unit.
Area $=$ length $\times$ breadth
Now metre is unit of length and breadth, so S.I. unit of area is obtained by multiplying the fundamental unit ' $m$ ' with itself. So, $m ^2$ is the derived unit of area.
3. Density = Mass/volume
S.I. unit of density i.e. $kg / m ^3$ is the derived unit of density because it can be obtained by combining two fundamental units kilogram and metre.

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