Units,Dimensions,Conversion and Significant digits in physics

Measurement:
The method of comparing any amount of a physical quantity with standard amount of same kind is called measurement. Measurement of a physical quantity consists of a numerical value (n) and a unit(u)
Therefore,
Measurement=Numerical Value(n)*Unit(u)

Unit:
There are 3 kinds of unit.
a) Fundamental unit :
    The units of fundamental quantities that cann't be derived from other units.
    Example:kg,meter,second etc.
    It is 7 in number.
b)Supplementary units:
    Example: Units of plane angle and solid angle.
c) Derived units:
    The units derived from fundamental and supplementary units.
    Example: Joule, Pascal, Newton etc.

 Systems of Units:
 There are four system of units.
 a) CGS System: In this system units for length , mass and time are centimeter(m),gram(m) and              seconds(s) respectively.
 b) FPS System: Units for length ,mass and time are Foot(ft), pound(lb) and second(s) respectively.
 c) MKS System: Units for length for length, mass and time are meter(m), Kilogram(kg) and                    second(s) respectively.
 d) SI System: In this system, there are seven fundamental quantities and fundamental units.


Fundamental Units (In SI System):

Physical Quantity
Units
Symbol
Length
mass
time
temperature
luminosity
electric current
amount of substance
Meter
kilogram
second
kelvin
candela
ampere
mole
M
kg
s
k
cd
a
mol

Supplementary Units
:

Physical Quantity
Units
Symbol
Plane angle
Solid angle
Radian
steradian
r
sr






Conversion Factor:

1litre       = 10-3 m3
1 g/cm3    = 103 kg/ m3
1 N           = 105 dyne
1 atm       = 1.01*105 N/M2
1hp           = 746w
1cal          = 4.2J
1Kwh        = 3.6*106 J

Dimensions and Dimensional Formulae:
·         The dimensions of a derived unit may be defined as the powers to which the fundamental units of mass, length and time must be raised to represent it.
For example:
Velocity=displacement/time
·         Thus the dimensions of the unit of velocity are one in length and -1 in time. Its dimension in mass is zero.
·         Work, energy ,quantity of heat , quantity of light, internal energy, torque each has dimensional formula ML2T-2 (kgm2/s2)
·         Velocity, Speed, distance covered in nth second have same dimensional formula m0LT-1 (M/S).
·         Pure numbers are dimensions.
Dimensions of Some Physical Quantities:

S.N
Physical Quantity
Dimensions
SI units
1
Density (D=M/V)
[ML-3]
Kg m-3
2
Force (F=Ma)
[MLT-2]
Kgms-2
3
Linear momentum (P=MV)
[MLT-1]
Kgms-1
4
Work or Energy(W=F*D)
[ML2T-2]
Kgm2s-2
5
Power (P=w/t)
[ML2T-3]
Kgm2s-3
6
Pressure (P=F/A)
[ML-1T-2]
Kgm-1s-2(N/M2)
7
Impulse(=F*t)
[MLT-1]
Kgms-1
8
Strain
[M0L0T0]
No Unit
9
Frequency (f)
[T1]
Hz
10
Stress (F/A)
[ML-1T2]
Kgm-1s-2

2 comments:

  1. It was really great blog provide helpful information !
    what is dimensional formula?

    ReplyDelete
    Replies
    1. Thanks gopipatel for feedback.
      Definition of dimensional formula:
      Dimensional formula can be defined as an expression for the unit of a physical quantity in terms of the fundamental quantities. These fundamental quantities are mass (M), length (L), and time (T). The dimensional formula is expressed in terms of powers of M,L and T.

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