1.1 Physical Quantities : Different
quantities needed to describe the physical phenomenon or object are called
physical quantities. Examples: speed, length, mass, density, etc.
The physical quantities are divided in
two groups.
1. Fundamental quantities: Those
physical quantities which are independent to any other physical quantities. Eg.
Mass, length, time, etc.
2. Derived quantities: Those physical
quantities which are dependent on other physical quantities and obtained by
multiplying and dividing the fundamental quantities are called derived
quantities. Eg. Density, velocity, acceleration, force, etc.
1.2 Units: The physical
quantities are measured by comparing with some standard measurement of same
kinds are called units. The units are divided in two groups.
1. Fundamental units: Units of fundamental
quantities are called fundamental unit. These are independent to any other
units.
2. Derived units: Units of
derived quantities are called derived unit. These units are obtained by multiplying and dividing the
fundamental units.
System of measurement:
1.
CGS system: The system of measurement in which 3
fundamental quantities mass, length and time are measured in gm, cm and s
respectivily. All other derived quantities are also measured in terms of these
units of measurements.
2.
MKS system: The system of measurement in which 3
fundamental quantities mass, length and time are measured in kg, m and s
respectivily. All other derived quantities are measured in terms of these units
of measurement is called MKS system.
3.
FPS system: : The system of measurement in
which 3 fundamental quantities mass, length and time are measured in pound,
foot and second respectivily. All other derived quantities are measured in
terms of these units of measurement is called FPS system.
4.
International system units (SI): SI is an
abbreviation “Le systeme International d’ unites.” Which is French and
equivalent of international system of units. It is used widely throughout the
world in which seven different quantities are introduced as fundamental
quantities and their units as fundamental units.
|
|
Quantity
|
Unit
|
Symbol
|
|
1.
|
Mass
|
Kilogram
|
Kg
|
|
2.
|
Length
|
Meter
|
M
|
|
3.
|
Time
|
Second
|
S
|
|
4.
|
Temperature
|
Kelvin
|
K
|
|
5.
|
Electric
Current
|
Ampere
|
Amp
|
|
6.
|
Luminous
Intensity
|
Candela
|
Cd
|
|
7.
|
Amount
of Substance
|
Mole
|
Mol
|
Two more
quantities are introduced as supplementary quantities and their units as
supplementary unit.
|
1.
|
Plane
angle
|
Radian
|
Rad
|
|
2.
|
Solid
angle
|
Steradian
|
Sr
|
Prefixes of power ten:
|
Prefix
|
Abbreviation
|
Power of ten
|
|
Atto
|
A
|
-18
|
|
Femto
|
F
|
-15
|
|
Pico
|
P
|
-12
|
|
Nano
|
N
|
-9
|
|
Micro
|
µ
|
-6
|
|
Milli
|
M
|
-3
|
|
Centi
|
C
|
-2
|
|
Deci
|
D
|
-1
|
|
Kilo
|
K
|
3
|
|
Mega
|
M
|
6
|
|
Giga
|
G
|
9
|
|
Tera
|
T
|
12
|
|
Peta
|
P
|
15
|
|
Exa
|
E
|
18
|
Some useful practical units:
1.
Astronomical
unit (AU): Average distance between centre of earth and centre of sun.
2.
Par
Sec used to measure long distance and represents a parallactic second. One par
sec is the distance at which an arc of 1 AU long subtends an angle of 1῞.
l =1AU
∴
1 Par sec = 3.1 × 1016m
3.
Light year (ly):-
Distance traveled by light is vacuum in one year.
∴
1ly = 9.46 × 1015m
4.
1 inch = 2.54 cm
1
foot = 30.48 cm
1
yard = 91.44 cm
1
mile = 1.609 × 103
1
nautical mile = 1.852 × 103m
1
angstrom (1A0) =× 10-10m
1
Fermi = 1 femtometer = 1015m
For
area:
1
barn = 10-28m2
1
acre = 4047 m²
1
hectare = 104m²
For
mass:
1
tonne or metric ton = 1000 kg
1
quintal = 100 kg
1
slug = 14.57 kg
1 lb = 0.4536
1
chandra shekhar limit (CSL) = 1.4 times mass of sun
1
amu (atomic mass Unit) = 1.67× 10-27kg
For
time:
1
shake = 10-8sec
1
solar year = 365.25 days
For
pressure:
1
bar = 1 atmosphere pressure = 105N/m2
1
torr = 1 mm of Hg = 133 N/m²
1
atmospheric pressure = 760 mm of Hg = 760 torr.
Dimension:
The power of fundamental quantity involved in any physical quantity iis called
dimension of that physical quantity. The representation of physical quantity in
terms of fundamental quantities involved in it is called dimensional formula of
that phsical quantity. Three fundamental quantities mass, length and time are
represented by [M], [L] and [T] respectively. All other derived quantities are
also expressed in terms of these representations.
Eg.
Force = ma = kgm/s² = [MLT-2]
The
dimension of mass is 1, length is 1 and time is -2 in force and force and the
representation [MLT-2] is called dimensional formula of force.
Dimensional
formula of some quantities:
|
SN
|
Physical
quantity
|
Formula
|
Dimensional
formula
|
Unit
|
|
1.
|
Density
|
Mass
Volume
|
[ML-3]
|
Kgm-3
|
|
2.
|
Specific
Gravity
|
Density
of body
Density
of water at 4°C
|
Dimensionless
|
-------------
|
|
3.
|
Linear
momentum
|
M
× v
|
[MLT-1]
|
Kgms-1
|
|
4.
|
Impulse
|
F×t
|
[MLT-1]
|
Ns
|
|
5.
|
Pressure
|
F/A
|
[ML-1T-2]
|
Nm-2
|
|
6.
|
Universal
Gravitational
Constant
|
G
= Fr2
m1m2
|
[M-1L3T-2]
|
Nm2/Kg2
|
|
7.
|
Work
|
F
× d
|
[ML2T-2]
|
Nm
|
|
8.
|
Moment
of force
|
F
× r
|
[ML2T-2]
|
Nm
|
|
9.
|
Power
|
w/t
|
[ML2T-3]
|
W
|
|
10.
|
Surface
tension
|
F/l
|
[ML0T-2]
|
Nm-1
|
|
11.
|
Surface
energy
|
Energy
|
[ML2T-2]
|
J
|
|
12.
|
Force
Constant
|
K=
F/x
|
[ML0T-2]
|
Nm-1
|
|
13.
|
Upthrust
|
Force
|
[MLT-2]
|
N
|
|
14.
|
Stress
|
F/A
|
[ML-1T-2]
|
Nm-2
|
|
15.
|
Strain
|
e/L
|
Dimensionless
|
---------
|
|
16.
|
Modulus
of elasticity
|
Stress
Strain
|
[ML-1T-2]
|
Nm-2
|
|
17.
|
Radius
of gyration
|
|
[L]
|
M
|
|
18.
|
Moment
of inertia
|
Mr²
|
[ML2T0]
|
Kgm2
|
|
19.
|
Angle
|
θ
= l/r
|
Dimensionless
|
Rad
|
|
20.
|
Angular
acceleration
|
α
= θ/r
|
[T-2]
|
rad/s2
|
|
21.
|
Angular
velocity
|
ω=
θ/t
|
[T-1]
|
rad/s
|
|
22.
|
Angular
momentum
|
L= Iω
|
[ML2T-1]
|
Kgm2s-1
|
|
23.
|
Torque
|
T=Iα
|
[ML2T-2]
|
Nm
|
|
24.
|
Frequency
|
f
= 1/t
|
[T-1]
|
s-1or
Hz
|
|
25.
|
Velocity
gradient
|
Dv
Dx
|
[T-1]
|
s-1
|
|
26.
|
Rate
of flow
|
V/t
|
[L3T-1]
|
m3s-1
|
|
27.
|
Planck’s
constant
|
h
= E/f
|
[ML2T-1]
|
Js
|
|
28.
|
Mass
per unit length
|
M/l
|
[ML-1]
|
Kgm-1
|
|
29.
|
Specific
latent heat
|
L=Q/m
|
[L2T-2]
|
JKg-1
|
|
30.
|
Thermal
conductivity
|
K=Q/{t.A(dθ/dl)}
|
[MLT-3K-1]
|
wm-1K-1
|
|
31.
|
Universal
gas
Constant
|
R
= PV
Nt
|
[ML2T-2K-1mol-1]
|
Jmol-1K-1
|
|
32.
|
Boltzman
Constant
|
k
= R
NA
|
[ML2T-2K-1]
|
JK-1
|
|
33.
|
Entropy
|
S=dQ/T
|
[ML2T-2K-1]
|
JK-1
|
|
34.
|
Charge
|
Q=It
|
[AT]
|
C
|
|
35.
|
Electric
dipole
Moment
|
(q.2l)
|
[ALT]
|
Cm
|
|
36.
|
Current
density
|
J=I/A
|
[AL-2]
|
Am-2
|
|
37.
|
Permittivity
|
ℇ0
= cd
A
|
[M-1L-3T4A2]
|
Fm-1
|
|
38.
|
Magnetic
flux
|
Φ
= BA
|
[M1L2T-2A-1]
|
Wb
|
|
39.
|
Permeability
|
μ
= 2BR/I
|
[M1L1T-2A-2]
|
Hm-1
|
|
40.
|
Specific
heat
Capacity
|
S
= Q/(mΔθ)
|
[L2T-2K-1]
|
J/kg-k
|
|
41.
|
Capacitance
|
c=4πε0r
|
[M-1L-2T4A2]
|
F
|
|
42.
|
Resistance
|
R=V/I
|
[M1L2T-3A-2]
|
Ω
|
|
43.
|
Magnetic
field
Induction
|
B
= F/(Il)
|
[MT-2A-1]
|
T
|
|
44.
|
Inductance
|
L
= E/(dI/dt)
|
[M1L2T-2A-2]
|
H
|
|
45.
|
Resistance
|
(RC)
|
[T]
|
S
|
|
46.
|
Inductance
Resistance
|
(L/R)
|
[T]
|
S
|
|
47.
|
√(inductance×capacitance)
|
√(LC)
|
[T]
|
S
|
Dimensionless
quantities:
Strain,
Coefficient of friction, Mechanical equivalent of heat, Poisson’s ratio, Angle
and solid angle, Relative density, Refractive index, Emissivity, Magnetic
susceptibility, Dielectric constant, Relative permeability, Relative
permittivity, Loudness.
Error
Measurement :
Error
in a combined equation X = K (ambn/cp)
(i)
Maximum or permissible
Relative error
(Δx/x)= m(Δa/a) + n(Δb/b)+
p(Δc/c)
(ii)
Maximum or permissible
percentage error
(Δx/x)
× 100% = {m(Δa/a)+ n(Δb/b)+ p(Δc/c)} × 100%
Where (Δa/a),(Δb/b) and
(Δc/c) are errors in measuring a, b and c.
Note: (-ve
is not considered in error i.e -p(Δc/c) for denominator term.)
