Units and Dimension, JEE Main Notes JEE Notes | EduRev

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In order to make the measurement of a physical quantity we have, first of all, to evolve a standard for that measurement so that different measurements of same physical quantity can be expressed relative to each other. That standard is called a unit of that physical quantity.
System of Units:
(a) C.G.S (Centimeter-Grand-Second) system.
(b) F.P.S. (Foot-Pound-Second) system.
(c) M.K.S. (Meter-Kilogram--Second) system.
(d) M.K.S.A. (Meter-Kilogram-Second-Ampere) unit.
Dimensional Formula:
Dimensional formula of a physical quantity is the formula which tells us how and which of the fundamental units have been used for the measurement of that quantity.
How to write dimensions of physical quantities:
(a) Write the formula for that quantity, with the quantity on L.H.S. of the equation.
(b) Convert all the quantities on R.H.S. into the fundamental quantities mass, length and time.
(c) Substitute M, L and T for mass, length and time respectively.
(d) Collect terms of M,L and T and find their resultant powers (a,b,c) which give the dimensions of the quantity in mass, length and time respectively.
Characteristics of Dimensions:
(a) Dimensions of a physical quantity are independent of the system of units.
(b) Quantities having similar dimensions can be added to or subtracted from each other.
(c) Dimensions of a physical quantity can be obtained from its units and vice-versa.
(d) Two different physical quantities may have same dimensions.
(e) Multiplication/division of dimensions of two physical quantities (may be same or different) results in production of dimensions of a third quantity.

Physical Quantity
Symbol
Dimension
Measurement Unit
Unit
Length
S
L
Meter
M
Mass
M
M
Kilogram
Kg
Time
T
T
Second
Sec
Electric Charge
Q
Q
Coulomb
C
Luminous Intensity
I
C
Candela
Cd
Temperature
T
K
Kelvin
Ok
Angle
Q
None
Radian
None

Mechanical Physical Quantities (derived)

Physical Quantity
Symbol
Dimension
Measurement Unit
Unit
Area
A
L2
square meter
m2
Volume
V
L3
cubic meter
m3
velocity
v
L/T
meter per second
m/sec
angular velocity
w
T-1
radians per second
1/sec
acceleration
a
LT-2
meter per square second
m/sec2
angular acceleration
a
T-2
radians per square
1/sec2
Force
F
MLT-2
Newton
Kg m/sec2
Energy
E
ML2T-2
Joule
Kg m2/sec2
Work
W
ML2T-2
Joule
Kg m2/sec2
Heat
Q
ML2T-2
Joule
Kg m2/sec2
Torque
t
ML2T-2
Newton meter
Kg m2/sec2
Power
P
ML2T-3
watt or joule/sec
Kg m2/sec3
Density
D or ρ
ML-3
kilogram per cubic meter
Kg/m3
pressure
P
ML-1T-2
Newton per square meter
Kg m-1/sec2
impulse
J
MLT-1
Newton second
Kg m/sec
Inertia
I
ML2
Kilogram square meter
Kg m2
luminous flux
f
C
lumen (4Pi candle for point source)
cd sr
illumination
E
CL-2
lumen per square meter
cd sr/m2
entropy
S
ML2T-2K-1
joule per degree
Kg m2/sec2K
Volume rate of flow
Q
L3T-1
cubic meter per second
m3/sec
kinematic viscosity
n
L2T-1
square meter per second
m2/sec
dynamic viscosity
m
ML-1T-1
Newton second per square meter
Kg/m sec
specific weight
g
ML-2T-2
Newton per cubic meter
Kg m-2/sec2

Electrical Physical Quantities (derived)

Electric current
I
QT-1
Ampere
C/sec
emf, voltage, potential
E
ML2T-2Q-1
Volt
Kg m2/sec2C
resistance or impedance
R
ML2T-1Q-2
ohm
Kgm2 /secC2
Electric conductivity
s
M-2L-2TQ2
mho
secC2/Kg m3
capacitance
C
M-1L-2T2 Q2
Farad
sec2C2/Kgm2
inductance
L
ML2Q-2
Henry
Kg m2 /C2
Current density
J
QT-1L-2
ampere per square meter
C/sec m2
Charge density
r
QL-3
coulomb per cubic meter
C/m3
magnetic flux, Magnetic induction
B
MT-1Q-1
weber per square meter
Kg/sec C
magnetic intensity
H
QL-1T-1
ampere per meter
C/m sec
magnetic vector potential
A
MLT-1Q-1
weber/meter
Kg m/sec C
Electric field intensity
E
MLT-2Q-1
volt/meter or newton/coulomb
Kg m/sec2 C
Electric displacement
D
QL-2
coulomb per square meter
C/m2
permeability
m
MLQ-2
henry per meter
Kg m/C2
permittivity,
e
T2Q2M-1L-3
farad per meter
sec2C2/Kgm3
dielectric constant
K
M0L0T0
None
None
frequency
f or n
T-1
Hertz
sec-1
angular frequency
W
T-1
radians per second
sec-1
Wave length
l
L
Meters
M

Principle of homogeneity:
It states that “ the dimensional formulae of every term on the two sides of a correct relation must be same.” 

Types of error:
(a) Constant errors:- An error is said to be constant error if it affects, every time, a measurement in a similar manner.
(b) Systematic errors:- Errors which come into existence by virtue of a definite rule, are called systematic errors.
(c) Random error or accidental error:- Error which takes place in a random manner and cannot be associated with a systematic cause are called random or accidental errors.
(d) Absolute error:-  Units and Dimension, JEE Main Notes JEE Notes | EduRev

Relative Error:
Units and Dimension, JEE Main Notes JEE Notes | EduRev

Percentage Error:-
Units and Dimension, JEE Main Notes JEE Notes | EduRev

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