Units And Dimensions-Physical Quantities

Units And Dimensions-Physical Quantities

MULTIPLE & SUB-MULTIPLE FACTORS:
    Prefixes for multiples and submultiples of units are used to more conveniently express very large and very small numbers.
    Depending upon the magnitudes of physical quantities we measure, we have to use different multiplication factors suitable for that particular case.Here let us see some widely used multiplication factors.
S.I. Prefixes:
    In physics we have to deal from very small (micro) to very large (macro) magnitudes as one side we talk about the atom while on the other side of universe, e.g., the mass of an electron is 9.1 \( \times \) 10^–31kg while that of the sun is 2 \( \times \) 10³⁰kg. 
To express such large or small magnitudes simultaneously we use the following prefixes:

Practical Units:
(1) Length :
    (i) 1 Fermi         = 1 fm = 10^–15 m 
    (ii) 1 X-ray unit     = 1XU = 10^–13 m 
    (iii) 1 angstrom     = 1Å = 10^–10 m = 10^–8 cm = 10^–7 mm = 0.1   nm 
    (iv) 1 micron     = 1\( \mu \)m = 10^–6 m
    (v) 1 astronomical unit= 1 A.U.=1.49 x 10¹¹ m (or) 1.5 x 10¹¹m  =1.5 x10⁸ km
    (vi) 1 Light year     = 1 LY = 9.46 x10¹⁵ m
(vii) 1 Parsec     = 1pc = 3.26 light year
(2)  Mass :
    (i) Chandra Shekhar unit     : 1 CSU = 1.4 times the mass of sun = 2.8 x 10³⁰ kg 
    (ii) Metric ton                    : 1 Metric ton = 1000 kg 
    (iii) Quintal                        : 1 Quintal = 100 kg 
    (iv) Atomic mass unit (amu): 1 amu = 1.67 X 10^–27 kg 
                (or) mass of proton or neutron is of the order of 1 amu
(3) Time :
    (i) Year : It is the time taken by earth to complete 1 revolution around sun in 
    its orbit.
    (ii) Lunar month : It is the time taken by moon to complete 1 revolution around the earth in its orbit. 1 L.M. = 27.3 days
    (iii) Solar day     : It is the time taken by earth to complete one rotation about its axis with respect to sun. Since this time varies from day to day, 
    average solar day is calculated by taking average of the duration 
    of all the days in a year and this is called Average Solar day. 
        1 Solar day = 365.25 days
    (iv) Sedrial day     : It is the time taken by earth to complete one rotation about its axis with respect to a distant star. 
        1 Solar year = 366.25 Sedrial day = 365.25 average solar day 
        Thus 1 Sedrial day is less than 1 solar day.
    (v) Shake : It is an obsolete and practical unit of time.1 Shake = 10^{– 8} sec