Chapter 1 Units and Measurements Physics Derived from

Chapter 1 Units and Measurements

Physics: Derived from the Greek word “Fu which means nature. • Physics is a branch of science which deals with nature and natural phenomena. • Physics Quantity: any quantity that can be measured. e. g. Mass, Length, Time, Area, Volume etc. • Types of physical quantity: • (1) Fundamental Quantity • (2) Derived Quantity

• Fundamental Quantity: The quantity which is independent of other physical quantity. e. g. Mass, Length, Time etc. these are the basic quantities. • Derived Quantity: The quantity which can be derived from the fundamental quantities. E. g. Velocity, area, volume etc. • Unit: A standard of measurement chosen for a physical quantity. • Types of units: (1) Fundamental Units and (2) Derived Units

• (1) Fundamental Units: Units used for the measurement of fundamental physical quantities like mass, length, time etc. • (2) Derived Units: Units used for the measurement of derived physical quantities like velocity, area, volume etc. • System of units (A set of fundamental and derived units) Types of System of units: (1) F. P. S. System (2) C. G. S. System (3) M. K. S. System (4) S. I. System

Advantages of SI Units: It is (1) Coherent system (derived units obtained from fundamental units without introducing any numerical factor. ) (2) Rational system (only one unit is used for similar type of physical quantities) (3) Absolute system (no gravitational units used) (4) Metric system (5) Used to represent all branches of physics.

Dimensions of physical quantities: These are the powers to which the fundamental units of mass, length and time are to be raised to represent a derived unit of the physical quantity. e. g. dimensions for mass, length, time are [M], [L], [T] respectively. • Dimensional formula: An expression showing how and which of the fundamental units are required to represent the units of a physical quantity. E. g. dimensional formula for area and velocity are [M 0 L 2 T 0] and [M 0 L 1 T-1] respectively. • Dimensional equation: The equation obtained by equating a physical quantity to its dimensional formula. E. g. area[A]= [M 0 L 2 T 0] , volume[V]= [M 0 L 3 T 0]

Table for dimensional formulae S. No Physical Quantity Physical Formula Dimensional Formula SI Unit 1 Speed =Distance/Time [M 0 L 1 T-1] m/s 2 Velocity =Displacement/Time [M 0 L 1 T-1] m/s 3 Acceleration =Velocity/Time [M 0 L 1 T-2] m/s 2 4 Force = Mass × Acceleration [M 1 L 1 T-2] Kg m/s 2 OR Newton(N) 5 Density =Mass/Volume [M 1 L-3 T 0] Kg/m 3 6 Pressure =Force/Area [M 1 L-1 T-2] Kgm-1 s-2 7 Work =Force × Displacement [M 1 L 2 T-2] Kgm-2 s-2 Contd. .

S. No Physical Quantity Physical Formula Dimensional Formula SI Unit 8 Kinetic energy =(1/2)mv 2 [M 1 L 2 T-2] Kgm 2 s-2 9 Potential energy =mgh [M 1 L 2 T-2] Kgm 2 s-2 10 Plane Angle(θ) =Arc length/Radius [M 0 L 0 T 0] No unit 11 Impulse =Force × Time [M 1 L 1 T-1] Kgm 1 s-1 12 Stress =Force/Area [M 1 L-1 T-2] Kgm-1 s-2 13 Strain =Change in length/Original length [M 0 L 0 T 0] No unit 14 Momentum =Mass × velocity [M 1 L 1 T-1] Kgm 1 s-1

Principle of homogeneity of dimensions • It states that the dimensions of all the terms on both sides of a dimension equation must be same. • Thus we can say that a physical formula is dimensionally correct if the dimensions of both sides of its equation are same.

Applications of principle of homogeneity • Checking the correctness of a given physical equation and • Conversion of one system of units to another system

• Calculate the dimensional formula of energy from the equation E = 1/2 mv 2. Sol. Dimensionally, E = mass × (velocity)2. Since 2 1 is a number and has no dimension. or, [E] = M × (L/ T) 2 = ML 2 T – 2

To Convert Units Of A Physical Quantity From One System Of Units To Another : •

Convert a force of 1 N into dynes. Dimension of force[F]= [M 1 L 1 T-2] •