# International System of Units (SI) Units : Physics notes

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The International System of Units (SI), commonly known as the metric system, is the international standard for measurement.

The SI is made up of 7 base units that define the 22 derived units with special names and symbols. The SI plays an essential role in international commerce and is commonly used in scientific and technological research and development.

The international system of units was introduced to the public in 1960 as a result to earlier research that began in 1948. SI is based on the meter-kilogram second system of units (MKS).

### International System of units

The International System of units based on seven base unitsis at present internationally acceptedunit system and is widely used throughout the world. In computing any physical quantity the units for derived quantities involved in the relationships are treated as though they were algebraic quantities till the desired units are obtained

1. CGS System In this system, the unit of length is centimetre, the unit of mass is gram and the unit of time is second.
2. FPS System In this system, the unit of length is foot, the unit of mass is pound and the unit of time is second.
3. MKS System In this system, the unit of length is metre, the unit of mass is kilogram and the unit of time is second.
4. SI System This system contain seven fundamental units and two supplementary fundamental units. The SI units are used in all physical measurements, for both the base quantitiesand the derived quantities obtained from them. Certain derived units are expressed by means of SI units of special names such as joule, newton, watt etc.

Below is the international system of units.

#### Base Units

 Amount Unit name Unit symbol Definition Length Meter m The distance traveled by light in a vacuum in 1/299792458 second. Weight Kilogram kg This is the unit for weight. The mass of the international prototype kilogram. Time Second s The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. Current Ampere A The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10-7 newtons per meter of length. Thermodynamic temperature Kelvin K 1/273.16 of the thermodynamic temperature of the triple point of water. Substance amount Mole mol The amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. (Limited to objects with clarified composition.) Elementary entities are subatomic particles that compose matter and energy. Luminosity Candela cd The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

#### Supplementary Units

 Amount Unit name Unit symbol Definition Plane angle Radian rad Radian describes the plane angle subtended by an arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian. Solid angle Steradian sr A steradian is a solid angle at the center of a sphere subtending a section on the surface equal in area to the square of the radius of the sphere.

#### Derived Units

Derived units are a combination of base units and supplementary units and the mathematical symbols of multiplication and division.

 Amount Unit name Unit symbol Area Square meter m2 Volume Cubic meter m3 Speed Meter per second m/s Acceleration Meter per second squared m/s2 Wavenumber Reciprocal meter m-1 Density Kilogram per cubic meter kg/m3 Current density Ampere per square meter A/m2 Magnetic field strength Ampere per meter A/m Concentration (of amount of substance) Mole per cubic meter mol/m3 Specific volume Cubic meter per kilogram m3/kg Luminance Candela per square meter cd/m2

Some derived units are given unique names.

 Amount Unit name Unit symbol Composition Frequency Hertz Hz 1Hz=1s-1 Force Newton N 1N=1kg･m/s2 Pressure, stress Pascal Pa 1Pa=1N/m2 Energy, work, amount of heat Joule J 1J=1N･m Power, radiant flux Watt W W=1J/s Electric charge, amount of electricity Coulomb C 1C=1A･s Electric potential/electric potential difference, voltage, electromotive force Volt V 1V=1J/C Resistance (electrical) Ohm Ω 1Ω=1V/A Conductance (electrical) Siemens S 1S=1Ω-1 Magnetic Weber Wb 1Wb=1V･s Magnetic flux density, magnetic induction Tesla T 1T=1Wb/m2 Inductance Henry H 1H=1Wb/A Celsius temperature Degree Celsius ℃ 1t=T-To Luminous flux Lumen lm 1lm=1cd･sr Illuminance Lux lx 1lx=1lm/m2

SI unit prefixes indicating integer powers of ten

 Factor Prefix Symbol Factor Prefix Symbol 1018 exa E 10-1 deci d 1015 peta P 10-2 centi c 1012 tera T 10-3 milli m 109 giga G 10-6 micro µ 106 mega M 10-9 nano n 103 kilo k 10-12 pico p 102 hecto h 10-15 femto f 10 deka da 10-18 atto a

#### Non-SI units

 Amount Unit name Unit symbol Definition Time Minute min 1min=60s Hour h 1h=60min Day d 1d=24h Plane angle Degree ° 1°= (π/180) rad Minute ′ 1′= (1/60) ° Second ″ 1″= (1/60) ′ Volume Liter l, L 1l=1dm3 Weight Metric ton t 1t=103kg