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