"SUBJECT-PhysicsClass- 11Chapter– Units and MeasurementsThe comparison of any physical quantity with its standard unit iscalled measurement.Physical QuantitiesAll the quantities in terms of which laws of physics are described, and whosemeasurement is necessary are called physical quantities.Units?A definite amount of a physical quantity is taken as its standard unit.?The standard unit should be easily reproducible, internationally accepted.Fundamental UnitsThose physical quantities which are independent to each other are called fundamentalquantities and their units are called fundamental units.S.No. Fundamental Quantities Fundamental Units Symbol 1. Length metre m2. Mass kilogram kg3. Time second S4. Temperature kelvin kg5 Electric current ampere A6 Luminous intensity candela cd7 Amount of substance mole molSupplementary Fundamental UnitsRadian and steradian are two supplementary fundamental units. It measures planeangle and solid angle respectively.S.No. Supplementary Fundamental Quantities Supplementary Unit Symbol1 Plane angle radian rad2 Solid angle steradian SrDerived UnitsThose physical quantities which are derived from fundamental quantities are calledderived quantities and their units are called derived units.e.g., velocity, acceleration, force, work etc. Definitions of Fundamental UnitsThe seven fundamental units of SI have been defined as under.1.1 kilogram A cylindrical prototype mass made of platinum and iridium alloys of height39 mm and diameter 39 mm. It is mass of 5.0188 x 1025 atoms of carbon-12.2.1 metre 1 metre is the distance that contains 1650763.73 wavelength of orange- red light of Kr-86.3.1 second 1 second is the time in which cesium atom vibrates 9192631770 times in anatomic clock.4.1 kelvin 1 kelvin is the (1/273.16) part of the thermodynamics temperature of the triplepoint of water.5.1 candela 1 candela is (1/60) luminous intensity of an ideal source by an area of cm’when source is at melting point of platinum (1760°C).6.1 ampere 1 ampere is the electric current which it maintained in two straightparallelconductor of infinite length and of negligible cross-section area placed one metreapart in vacuum will produce between them a force 2 x 10-7 N per metre length.7.1 mole 1 mole is the amount of substance of a system which contains a manyelementaryentities (may be atoms, molecules, ions, electrons or group of particles, as this andatoms in 0.012 kg of carbon isotope 6C12. Systems of UnitsA system of units is the complete set of units, both fundamental and derived, for allkinds of physical quantities. The common system of units which is used in mechanicsare given below:1.CGS System In this system, the unit of length is centimetre, the unit of mass is gramand 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 theunit of time is second.3.MKS System In this system, the unit of length is metre, the unit of mass is kilogramand the unit of time is second.4.SI System This system contain seven fundamental units and two supplementaryfundamental units.Relationship between Some Mechanical SI Unit and Commonly Used UnitsS.No. Physical Quantity Unit (a) 1 micrometre = 10-6 m1 Length (b) 1 angstrom =10-10 m2 Mass (a) 1 metric ton = 103 kg(b) 1 pound = 0.4537 kg(c) 1 amu = 1.66 x10-23 kg3 Volume 1 litre = 10-32 m3 (a) 1 dyne = 10-5 N4. Force (b) 1 kgf = 9.81 N (a) 1 kgfm2 = 9.81Nm-2(b) 1 mm of Hg = 133 Nm-25. Pressure (c) 1 pascal = 1 Nm-2 (d) 1 atmosphere pressure = 76 cm of Hg = 1.01 x 105 pascal(a) 1 erg =10-7 J(b) 1 kgf-m = 9.81 J6. Work and energy (c) 1 kWh = 3.6 x 106 J (d) 1 eV = 1.6 x 10-19 J(d) 1 kgf- ms-1 = 9.81W7. Power 1 horse power = 746 W Some Practical Units1.1 fermi =10-15 m2.1 X-ray unit = 10-13 m3.1 astronomical unit = 1.49 x 1011 m (average distance between sun and earth)4.1 light year = 9.46 x 1015 m5.1 parsec = 3.08 x 1016 m = 3.26 light year Some Approximate MassesObject KilogramOur galaxy 2 x 1041Sun 2 x 1030Moon 7 x 1022Asteroid Eros 5 x 1015DimensionsDimensions of any physical quantity are those powers which are raised onfundamental units to express its unit. The expression which shows how and which ofthe base quantities represent the dimensions of a physical quantity, is called thedimensional formula.Dimensional Formula of Some Physical QuantitiesPhysical Dimensional MKSS.No. Quantity Formula Unit1 Area [L2] metre22 Volume [L3] metre33 Velocity [LT-1] ms-14 Acceleration [LT-2] ms-25 Force [MLT-2] newton (N) 6 Work or energy [ML2T-2] joule (J)7 Power [ML2T-3] J s-1 or watt8 Pressure or stress [ML-1T-2] Nm-29 Linear momentum or Impulse [MLT-1] kg ms-110 Density [ML-3] kg m-311 Strain Dimensionless Unitless12 Modulus of elasticity [ML-1T-2] Nm-213 Surface tension [MT-2] Nm-114 Velocity gradient T-1 second-115 Coefficient of velocity [ML-1T-1] kg m-1s-116 Gravitational constant [M-1L3T-2] Nm2/kg217 Moment of inertia [ML2] kg m218 Angular velocity [T-1] rad/s19 Angular acceleration [T-2] rad/S220 Angular momentum [ML2T-1] kg m2S-1kcal kg-1K- 21 Specific heat L2T-2?-1122 Latent heat [L2T-2] kcal/kg23 Planck’s constant ML2T-1 J-s24 Universal gas constant [ML2T-2?-1] J/mol-K\r\n\r\nPropagation of Error\r\n(i) Error in Addition or Subtraction Let x = a + b or x = a – b\r\nIf the measured values of two quantities a and b are (a ± Δa and (b ± Δb), then maximum absolute error in their addition or subtraction.\r\n"