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Fundamental Quantity Derived Quantity Limitations of Dimensional Analysis
The physical quantities which are Those quantities which can (i) It does not predict the coefficient associated with a
not derised any other physical be expressed in terms of physical quantity in a relation
quantities. E.g., Mass, Length, fundamental/base quantities.
Time Temperature, current, E.g., velocity acceleration, eg, v= u + 1 at & v = u + at
luminous Intensity & mole 3 5
force etc.,
Both are dimensionally valid.
(ii) It does not derive any relations involving trigonometric,
SYSTEM OF UNITS
logarithmic or exponential functions
(a) FPS System: Here length is measured in foot, mass in 2
E.g. P = P0e–bt cannot be derived dimensionally.
pounds and time in second.
(iii) It does not give any information about dimensionall
(b) CGS System: In this system, length is measured in cm,
constants in an expression and doesnot tell the nature of
mass is measured in g and time is measured in second.
a quantity (vector/scalar) in a relation.
(c) MKS System: In this system, length is measured in metre,
mass is measured in kg and time is measured in second. SIGNIFICANT FIGURES OR DIGITS
(d) SI System: This is the standard system of units used 1. Rules to find out the number of significant figures:
internationally . Here length is measured in metre, mass in
I Rule:All the non-zero digits are significant E.g. 1984 has
kg and time in second.
4 SF.
PRINCIPLE OF HOMOGENEITY II Rule: All the zeros between two non-zero digits are
According to this, the physical quantities having same dimensions significant. E.g. 10806 has 5 SF.
can be added or subtracted with each other and for a given equation, III Rule: All the zeros to the left of first non-zero digit are
dimensions of both sides must be same. not significant. E.g.00108 has 3 SF.
B IV Rule: If the number is less than 1, zeros on the right of the
For eg, in equation F
= A m+ +C ,
v decimal point but to the left of the first non-zero digit are not
significant. E.g. 0.002308 has 4 SF.
all the three terms of R.H.S have same dimensions as that of force
on L.H.S. V Rule : The trailing zeros (zeros to the right of the last non-
zero digit) in a number with a decimal point are significant.
DIMENSIONS E.g. 01.080 has 4 SF.
The fundamental or base quantities along with their powers needed VI Rule: The trailing zeros in a number without a decimal
to express a physical quantity is called dimensional formula. point are not significant e.g. 010100 has 3 SF. But if the
E.g.: [F] = [MLT–2] are dimensions of force. number comes from some actual measurement then the
trailing zeros become significant. E.g. m = 100 kg has 3
Use of Dimensional Analysis SF.
(i) To check the correctness of a given formula.
VII Rule: When the number is expressed in exponential
(ii) To establish relation between quantities dimensionally. form, the exponential term does not affect the number of S.F.
(iii) To convert the value of a quantity from one system of For example in x = 12.3 = 1.23 × 101 = .123 × 102 = 0.0123 ×
units to other system. 103 = 123 × 10–1, each term has 3 SF only.
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