Units and Measurements

1. International System of Units 

Measurement

It is the process of assigning a number to an attribute (or phenomenon) according to a rule or set of rules.

Units

• A unit is the chosen standard of measurement of quantity, which has the same nature as the quantity.
• To express any physical quantity completely, we need the numerical value and the unit (u).

Physical quantity = nu

Fundamental Units: Units for fundamental or base quantities (length, mass and time)

Derived Units: Units obtained from fundamental units

Example:

Unit of speed (ms⁻¹)

Speed

∴Unit of speed

Systems of Units

• CGS System: Base units for length, mass and time in this system are centimeter, gram and second respectively.
• FPS System: Base units for length, mass and time in this system are foot, pound and second respectively.
• MKS System: Base units in this system are metre, kilogram and second.
• International System (SI) of Units: Based on seven base units; at present the internationally accepted system

SI Base Quantities and Units

• Length − metre (m)
• Mass − kilogram (kg)
• Time − second (s)
• Electric current − ampere (A)
• Thermodynamic temperature − kelvin (K)
• Amount of substance − mole (mol)
• Luminous intensity − candela (cd)

Derived Units

• The units of different physical quantities can be derived from the seven basic fundamental units. These are called derived units.
• Some common derived units are mentioned in the given table.

S.No.	Physical Quantity	Relationship with Fundamental Unit	Symbol
1.	Volume	Length cube	m3
2.	Density	Mass per unit volume	kg m−3
3.	Velocity	Distance covered in unit time	ms−1
4.	Acceleration	Velocity changes per unit time	ms−2
5.	Force	Mass × Acceleration	kg ms−2
6.	Work	Force × Distance travelled	kg m2s−2
7.	Pressure	Force per unit area	kg m−1s−2

 

We have seen various objects as large as a mountain to as small as a speck. Therefore, to measure such large and small quantities, we have to use a simple method.

Example: Diameter of the sun = 1,391,000,000 m Diameter of a hydrogen atom = 0.000,000,000,106 m Thus, when we are using metre, we find that the content is either quiet bulky or very small. At the same time, it is very inconvenient. Therefore, to counter this, we use a standard form of expression as: Diameter of the sun = 1,391,000,000 m = 1.39 × 109 m Diameter of a hydrogen atom = 0.000,000,000,106 m = 1.06 × 10−10 m

The exponential part of a particular measurement is called the order of magnitude of a quantity.

The prefixes and symbols for such order of magnitude are listed in the given table.

Multiple	Prefix	Symbol
10−15	femto	f
10−12	pico	p
10−9	nano	n
10−6	micro	µ
10−3	milli	m
10−2	centi	c
10−1	deci	d
103	kilo	k
106	mega	M
109	giga	G

2. Measurement of Length

Measurement of Length

• Measurement of Large Distances

• Method used − Parallax method
• Parallax − Name given to the apparent change in position of an object with respect to the background, when the object is seen from two different positions

Far-away object (S) is observed from two different positions (A and B).

Distance between the two observation points is called basis (b).

The angle θ is called parallax angle. When θ is very small, we can consider the line segment AB as an arc of length b having radius D. By geometry,