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PHYSICAL QUANTITY
The quantities which can be measured by an instrument and by means of which we can describe the laws of physics are called physical quantities.
Fundamental quantities:
Although the number of physical quantities that we measure is very large, we need only a limited number of units for expressing all the physical quantities since they are interrelated with one another. So, certain physical quantities have been chosen arbitrarily and their units are used for expressing all the physical quantities, such quantities are known as
Fundamental, Absolute or Base Quantities (such as length, time and mass in mechanics)
(i) All other quantities may be expressed in terms of fundamental quantities.
(ii) They are independent of each other and cannot be obtained from one another.
An international body named General Conference on Weights and Measures chose seven physical quantities as fundamental:
(1) Length
(2) Mass
(3) Time
(4) Electric current,
(5) Thermodynamic temperature
(6) Amount of substance
(7) Luminous intensity.
Note:
These are also called as absolute or base quantities. In mechanics, we treat length, mass and time as the three basic or fundamental quantities.
Derived: Physical quantities which can be expressed as combination of base quantities are called as derived quantities.
MANITUDE:
Magnitude of physical quantity = (numerical value) × (unit)
Magnitude of a physical quantity is always constant.
It is independent of the type of unit.
UNIT:
Measurement of any physical quantity is expressed in terms of an internationally accepted certain basic reference standard called unit. The units for the fundamental or base quantities are called fundamental or base unit. Other physical quantities are expressed as combination of these base units and hence, called derived units.
A complete set of units, both fundamental and derived is called a system of unit.
3.1 Principle systems of unit
There are various system is use over the world:
CGS, FPS, SI (MKS) etc
Table 1: unit of some physical quantities in different system

Physical Quantity 
System 

CGS (Gaussian) 
MKS (SI) 
FPS (British) 

Fundamental 
Length 
centimetre 
meter 
foot 
Mass 
gram 
Kilogram 
Pound 

Time 
second 
second 
Second 

Derived 
Force 
Dyne 
Newton>N 
poundal 
Work or Energy 
erg 
joule>J 
ftpoundal 

Power 
erg/s 
Watt>W 
Ftponudal/s 
Supplementary units:
(1) Plane angle: radian (rad)
(2) Solid angle: steradian (sr)
* The SI system is at present widely used throughout the world. In IIT JEE only SI system is followed.
Definition of some important SI
Units
Significant digits, rounding off & mathematical operation, Types of Errors
Whenever an experiment is performed, two kinds of errors can appear in the measured quantity.
(1) Random and (2) systematic errors
Error limits Q ± ∆Q is the measured quantity and ∆Q is the magnitude of its limit of error. This expresses the experimenter's judgement that the 'true' value of Q lies between Q  ∆Q and Q + ∆Q. This entire interval within which the measurement lies is called the range of error. Random errors are expressed in this form.
Absolute Error
Error may be expressed as absolute measures, giving the size of the error in a quantity in the same units as the quantity itself. Least Count Error:  If the instrument has known least count, the absolute error is taken to be half of the least count unless otherwise stated. Error may be expressed as relative measures, giving the ratio of the quantity’s error to the quantity itself. In general,
We should know the error in the measurement because these errors propagate through the calculations to produce errors in results.
For example in the experiment on finding the focal length of a convex lens, the object distance (u) is found by subtracting the positions of the object needle and the lens. If the optical bench has a least count of 1 mrn, the error in each position will be 0.5mm. So, the error in the value of u will be 1 mm.
Addition and subtraction rule:
The absolute random errors add.
Thus if R = A + B, r = a + b
And
If R = A – B, r = a + b
Product and quotient rule: The relative random errors add.
SIGNIFICANT DIGITS
Significant figures are digits that are statistically significant. There are two kinds of values in science:
The way that we identify the proper number of significant figures in science are different for these two types.
MEASURED VALUES
Identifying a measured value with the correct number of significant digits requires that the instrument’s calibration be taken into consideration. The last significant digit in a measured value will be the first estimated position. For example, a metric ruler is calibrated with numbered calibrations equal to 1 cm. In addition, there will be ten unnumbered calibration marks between each numbered position. (Each equal to 0.1 cm). Then one could with a little practice estimate between each of those marking. (Each equal to 0.05 cm). That first estimated position would be the last significant digit reported in the measured value. Let’s say that we were measuring the length of a tube, and it extended past the fourteenth numbered calibration half way between the third and fourth unnumbered mark. The metric ruler was a meter stick with 100 numbered calibrations. The reported measured length would be 14.35 cm. Here the total number of significant digits will be 4.
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