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Physics And Measurement

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Physics and Measurement PDF Notes, Important Questions and Synopsis

SYNOPSIS

  • Physics domain:
  1. Macroscopic domain: This includes phenomena at the laboratory, terrestial and astronomical scales. Classical mechanics deals with the macroscopic domain.
  2. Microscopic domain: This includes atomic, molecular and nuclear phenomena. Quantum mechanics deals with the microscopic domain.
  • Four fundamental forces of nature:

Force

Relative strength

Range

Gravitational force

 10-39

Infinite

Nuclear force (weak)

 10-13

Very short, sub-nuclear size begin mathsize 12px style text ∼10 end text to the power of negative 16 end exponent end style

Electromagnetic force

 10-2

Infinite

Nuclear force (strong)

1

Short,  nuclear sizebegin mathsize 12px style text ∼10 end text to the power of negative 16 end exponent end style

  • Physical quantities:

  • Measure of physical quantity (Q) = numerical value of physical quantity (n) × size of unit (u) n1u1 = n2u2 = constant 

  • Fundamental quantities, SI unit and their symbols:

    Fundamental quantity

    SI unit

    Symbol

    Length

    metre

    m

    Mass

    kilogram

    kg

    Time

    second

    s

    Electric current

    ampere

    A

    Temperature

    kelvin

    K

    Amount of substance

    mole

    mol

    Luminous intensity

    candela

    cd

  • Conversion of units:
    Consider dimensions of a physical quantity as ‘x’ in mass, ‘y’ in length and ‘c’ in time. If the fundamental units in one system are M1, L1 and T1 and in another system are M2, L2 and T2,
    then
    begin mathsize 12px style text n end text subscript 1 open square brackets straight M subscript 1 to the power of straight x straight L subscript 1 to the power of straight y straight T subscript 1 to the power of straight z close square brackets straight equals straight straight n subscript 2 open square brackets straight M subscript 2 to the power of straight x straight L subscript 2 to the power of straight y straight T subscript 2 to the power of straight z close square brackets end style                 
  • Analysis of dimensional correctness:
    Every equation should be dimensionally balanced. This is called ‘principle of homogeneity’. The dimensions of each term must be the same on both sides of the equation.
  • Principle of homogeneity:
    According to the principle of homogeneity, dimensions of all terms in a physical expression should be the same.
  • Errors: 
    Errors are classified as (i) systematic errors and (ii) random errors.

  • If x1, x2, x3 … xn are the measured values of quantities in several measurements, then the mean is
    begin mathsize 12px style text x end text subscript mean equals fraction numerator straight x subscript 1 plus straight x subscript 2 plus straight x subscript 3. .. straight x subscript straight n over denominator straight n end fraction end style
  • Absolute errors in measured values are
    begin mathsize 12px style table attributes columnalign left end attributes row cell Δx subscript 1 equals straight x subscript 0 minus straight x subscript 1 comma end cell row cell Δx subscript 2 equals straight x subscript 0 minus straight x subscript 1 comma end cell row. row. row. row cell Δx subscript straight n equals straight x subscript 0 minus straight x subscript straight n comma end cell end table end style
  • If the quantity Z is expressed as a product of quantities A and B, then the maximum fractional error in Z is given by
    begin mathsize 12px style ΔZ over straight Z equals ΔA over straight A plus ΔB over straight B end style
  • If Z = AxByCz, then the maximum fractional error in Z is

    begin mathsize 12px style ΔZ over straight Z equals straight m ΔA over straight A plus straight n ΔB over straight B plus calligraphic l ΔC over straight C end style
 
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