Nature Of The Physical World And Measurement
Jan 13, 2015
Nature Of The Physical World And Measurement
Forces of Nature
Sir Issac Newton,“Force is the external agency applied on a
body to change its state of rest and motion”◦Gravitational force◦Electromagnetic force◦Strong nuclear force◦Weak nuclear force
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Physical Quantity
Fundamental Quantity
Length
Mass
Time
Electric current
Temperature
Luminous Intensity
Amount of substance
Plane angle
Solid angle
Derived Quantity
Area, Volume, Density
Expressing Larger And Smaller Physical Quantities
S.NO POWER OF TEN
PREFIX ABBREVIATION
1 10-15 Femto f
2 10-12 Pico p
3 10-9 Nano n
4 10-6 Micro μ
5 10-3 Milli m
6 10-2 Centi c
7 10-1 Deci d
8 101 Deca da
9 102 Hecto h
10 103 Kilo k
11 106 Mege M
12 109 Giga G
13 1012 Tera T
14 1015 peta P
Light YearIt is the distance travelled by light
in one year in vaccum. 1 Light Year = 9.467 x 1015mAstronomical unit
It is the mean distance of the centre of the sun from the centre of the Earth.
1 Astronomical Unit (AU) = 1.496 X 1011m
LIGHT YEAR AND ASTRONOMICAL UNIT
Determination of DistanceLaser pulse method
Determination of mass
Determination of timeAtomic clocks – 1013 secQuartz clocks – 109 sec
Significant figures
The number of meaning digits in a number is called the number of significant figures.
RULES
1. All the non- zero digits in a number are significant.
2. All the zeros between two non-zeros digits are significant, irrespective of the decimal point.
3. The zeros at the end without a decimal point are not significant.
4. The trailing zeros in a number with a decimal point are significant
Significant Figures Examples
0.0631 – Three Significant Figures. 56700 - Three Significant Figures.0.00123 – Three Significant Figures.30.00 – Four Significant Figures. 6.320 – Four Significant Figures. 600900 – Four Significant Figures.346.56 – Five Significant Figures 5212.0 – Five Significant Figures.
Rounding Off
If the insignificant digit is more than 5,◦The preceding digit is raised by 1.
If the insignificant digit is not more than 5,◦There is no change.
If the insignificant digit is 5◦Even
there is no change.◦Odd
The preceding digit is raised by 1.
Rounding Off Examples
53.473 kg – 53.6 kg
0.575 m – 0.58 m
0.495 – 0.50
Errors in Measurement♣ Constant Errors
It is due to faulty calibration of the scale in the measuring instrument.
♣ Systematic Errors
These are errors which occur due to a certain pattern or system.♣ Gross Errors
a. Improper setting of the instrument.
b. Wrong recording of the observation.
c. Not taking into account sources of error and precautions.
d. Usage of wrong values I the calculation.♣ Random Errors
It is very common that repeated measurement of a quantitative values which are slightly different from each other.
Dimensional Analysis
Fundamental Quantity
Dimension
Length L
Mass M
Time T
Temperature K
Electric current A
Luminous intensity cd
Amount of substance mol
Dimensions of a physical quantity are the powers to which the fundamental quantities must be raised.
Dimensional Quantities◦ Dimensional variables are those physical quantities which
possess dimensions but do not have a fixed value.
Ex. Velocity, force, etc.,
Dimensionless Quantities◦ There are certain quantities which do not possess dimension .
Ex. Strain, angle, specific gravity, etc.,
Principle of homogeneity of dimensions◦ An equation is dimensionally correct if the dimensions of the
various terms on either side of the equation are the same.
Ex. A+ B = C is valid only if the dimensions of A, B & C are the same.
Uses of Dimensional Analysis
Convert a physical quantity from one system of units to another.
Check the dimensional correctness of a given equation.
Establish a relationship between different physical quantities in an equation.
Limitations of Dimensional Analysis
The value of dimensionless constants cannot be determined by this method.
This method cannot be applied to equations involving exponential and trigonometric functions.
It cannot be applied to an equation involving more than three physical quantities.
It can check only whether a physical relation is dimensionally correct or not. It cannot tell whether the relation is absolutely correct or not.