Derived units — lesson. Science State Board, Class 9.

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In the previous exercises, we have discussed the basics of Units and SI units. In this exercise, we are going to look at the basics of derived units.

What are derived units?

A derived unit is a unit that results from a mathematical combination of SI base units.

SI is built on seven fundamental standards called base units. All other SI units are derived by multiplying, dividing or powering the base units in various combinations.

For example:

The area is length multiplied by width and has the unit of $m^{2}$ .
Mechanical work is a force applied, multiplied by the distance moved and has the unit newton metre. It is written as $Nm or J$ .
Velocity is displacement divided by time and has the unit metre per second. It is written as $m s^{- 1}$ .

S. No.	Physical Quantity	Expression	Unit
1	Area	$length \times breadth$	$m^{2}$
2	Volume	$area \times height$	$m^{3}$
3	Density	$\frac{mass}{volume}$	$kg m^{- 3}$
4	Velocity	$\frac{displacement}{time}$	$m s^{- 1}$
5	Momentum	$mass \times velocity$	$kg {ms}^{- 1}$
6	Acceleration	$\frac{velocity}{time}$	$m s^{- 2}$
7	Force	$mass \times acceleration$	$kg {ms}^{- 2} or N$
8	Pressure	$\frac{force}{area}$	$N m^{- 2} or Pa$
9	Energy (Work)	$force \times distance$	$Nm or J$
10	Surface tension	$\frac{force}{length}$	$N m^{- 1}$

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5. Derived units

Theory: