Chapter-2 dimension of physical quantities UNITS AND MEASUREMENT


Previous Knowledge
› ‘Physical quantities’ are of two types- ‘Base’ or ‘Fundamental 
quantity’ and ‘Derived quantities’. 
› We have seven fundamental quantities- “Length, Mass, Time, 
Electric current, Thermodynamic Temperature, Amount of 
substance, Luminous intensity”. 
DIMENSIONS OF PHYSICAL QUANTITIES
All physical quantities can be measured and expressed in terms of 
the seven fundamental or base quantities. we call these base 
quantities as the seven dimensions of the physical world, which are 
denoted with square brackets [ ]. Thus, length has the dimension [L],
mass [M], time [T], electric current [A], thermodynamic temperature
[K], luminous intensity [cd], and amount of substance [mol].

Let us start the dimension of a physical quantity with a simple 
example-‘Area’
We know that Area is a derived quantity, so that we can express Area
of an object as the product of length and breadth, or two lengths.
 ie Area=Length×Breadth
In dimensions format we can write
 [ Area]=[Length]×[Breadth]=[ Length]×[Length]=[L]×[ L]=[ L
2
]
** Note that using the square brackets [ ] round a quantity means 
that we are dealing with ‘the dimensions of’ the quantity.
Hence we can write [ Area]=[L
2
]=[ M
0
][ L
2
][T
0
]=[ M
0
L
2
T
0
]
Here Area has 2 dimensions in length and zero dimensions in other 
quantities, since area is independent of other base quantities. 
This [M
0
L
2
T
0
] is known as Dimensional formulae of Area.
(Dimensional formulae of a physical quantity is an expression 
showing the dimensions of the base quantities)
The powers in this dimensional formulae is called Dimensions of 
Area.
[ Area]=[M
0
L
2
T
0
] is the Dimensional Equation of Area.
(Dimensional equation is one which connects a physical quantity 
and its dimensional formulae)
The dimensions of a physical quantity are the powers (or exponents) 
to which the base quantities are raised to represent that quantity.
Similarly Dimensional analysis of Volume can be written as
[Volume ]=[Length]×[Breadth]×[ Height ]=[Length]×[Length]×[ Length]=[ L]×[ L]×[L]=[ L
3
]
Hence [Volume ]=[L
3
]=[M
0
L
3
T
]
  

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