Physical quantity , Fundamental quantities , Derived Units & Definitions of Base Units

Chapter Content :
1. Fundamental quantities , Derived Units & Definitions of Base Units
2. Dimensional Analysis & Uses of Dimensional equations
3. Significant figures , Rules of counting significant figure
4. Errors in Measurement
5. Vernier Callipers & Screw Gauge

Physical Quantity

A physical quantity is a quantity that can be measured i.e. a physical quantity is properly defined, has proper units, and its value can be measured by an instrument.
Physical quantities are classified as fundamental and derived quantities.

Fundamental Quantities

Fundamental quantities are those that are defined directly by the process of measurement only. They are not defined in terms of other quantities; their units are not defined in terms of other units. In mechanics we treat length, mass and time as basic or fundamental quantities.

Derived Units

The units of all other physical quantities, which can be obtained from fundamental units, are called derived unit.

System of units  Length Mass Time
F.P.S Foot pound second
C.G.S centimeter gram second
M.K.S(S.I) meter kilogram second

Illustration : Find the unit of speed.

Solution :

\displaystyle Speed = \frac{distance}{time} = m s^{-1}

Definitions of Base Units:

 Meter:
Since 1983, the standard metre is defined as the length of the path travelled by light in vacuum in (1/299,792,458) th part of a second.

 Kilogram:
Nowadays the standard kilogram is the mass of a cylinder made of platinum-iridium alloy and stored in a special vaule in the International Bureau of Weights and Measures at Sevres in France.

Second:
At present second is defined on the basis of an atomic clock, which uses the energy difference between the two lowest energy states of the cesium atom. When bombarded by microwaves of precisely the proper frequency, cesium atoms undergo a transition from one of these states to other. One second is defined as the time required for 9,192,631,770 cycles of this radiation

In physics SI system is based on seven fundamental and two derived units.

Basic Physical Quantities: Fundamental Unit:
Mass kilogram
Length meter
Time second
Temperature kelvin
Electric current ampere
Luminous intensity candela
Quantity of matter mole

 

Supplementary Physical Quantities Supplementary unit
Plane angle radian
Solid angle steradian

Some Practical units:

For the measurement of very large distance, the following three units are used.
(i) Astronomical Unit (AU) : It is the average distance of the centre of the sun from the centre of the earth.
1 AU = 1.5 × 1011 metre

(ii) Light year : It is defined as the distance traveled by light in vaccum in one year
1 light year = 3 × 108 × (365 × 24 × 60 × 60) metre

1 ly = 9.4 × 1015 metre

(iii) Par sec : It is defined as the distance at which an are 1 AU long subtends an angle of 1’’

1 par sec = 3.1 × 1016 metre

Illustration : Fill in the blank by suitable conversion of units
1 kg m2s-2 =….. g cm2s-2

Solution : 1kg m2s-2 = 1×103 g (102cm)2 s-2

= 107g cm2 s-2

Exercise 1: (i) What is the value of one micron in centimeter ?
(ii) What is the value of a pressure of 106 dynes/cm2 in S.I unit ?

Exercise 2:Fill in the blanks :
(a) The volume of a cube of side 1 cm is equal to …..m3
(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to …….(mm)2
(c) A vehicle moving with a speed of 18 km/h covers………m in 1 s
(d) The relative density of lead is 11.3. Its density is …….g cm3 or ……..kg m3.

Exercise 3: Fill in the blanks by suitable conversion of units :
(a) 1 kg m2 s2 = ….g cm2 s2
(b) 1 m = ….. ly
(c) 3.0 m s-2 = …. km h-2
(d) G = 6.67 × 10-11 N m2 (kg)-2 = …. (cm) 3 s-2 g-1

Exercise 4: A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2 s-2.
Suppose we employ a system of units in which the unit of mass equals α kg , the unit of length equals β m , the unit of time is γ s. Show that a calorie has a magnitude 4.2 α-1 β-2 γ2 in terms of the new units.

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