METHOD OF MEASUREMENT OF DIFFERENT PHYSICAL QUANTITIES (3)

Measurement of time


Time is measured by a wall clock, wrist watch, table clock. To measure a

fraction of time , stop watch is used.



Method of measurement of time by a clock


In our day to day life , time is measured by pendulum clock, whose function is based on the oscillation of a pendulum. In this type of clock, a metal rod is suspended from a rigid support. A heavy metal ball is suspended from the end of the rod. The time taken by the metal ball in one oscillation is regarded as 1 second. It consists of a circular dial which divided in 60 equal divisions.

Each division represents 1 minute. It is further divided into 12 equal parts, where each parts represents 1 hour. Hours are marked from 1 to 12 . In this clock long arm is the arm of minute and the short arm is the arm of hours. A spring is wound up with the help of key in old type of clock and by battery in digital clocks or battery operated clocks. The potential energy is converted to kinetic energy and rotates the arms of the clock.



Method of measurement of interval of time with the help of stop watch


Stop watch is used to measure the time interval between two events. It consists of a circular dial which is divided in 60 equal divisions. Each division represents 1 second. A long, light needle called second’s hand pivoted at the centre, rotates over the circular scale. A big circular dial also contains a small circular dial to read the time in minutes . The smaller dial graduated in 30 or 60 divisions and the small needle called the minute’s hand rotates over the scale. When the seconds hand completes one rotation, the minutes hand moves through one division or 1 minute.

A knob is provided at the top of the frame for winding the watch. By pressing the

Knob in succession, the watch can be started, stopped and both the needles can be

Brought to searting point for future use.

METHOD OF MEASUREMENT OF DIFFERENT PHYSICAL QUANTITIES (2)

Method for the measurement of volume of a liquid

The space occupied by a body is called the volume of that body.
The volume of a liquid in the laboratory is measured by the following
Measuring devices.
1.    Measuring cylinder
2.    Measuring flasks
3.    Burette
4.    Pipette
Measuring cylinder is commonly used to measure the volume of a liquid. It is 
a glass cylinder of uniform radius. The outer wall is graduated in cubic centimetre
and millimeter from the bottom upwards. It is available in different sizes. Before
measuring the volume of a liquid through measuring cylinder it is cleaned and
kept fixed vertically. The liquid whose volume has to measure is poured in it
and the reading of upper layer of the liquid is noted. This reading is the volume
of the liquid.


To determine the volume of an irregular solid heavier than and insoluble in water
                                 With the hep of measuring cylinder

To find the volume of an irregular shape of solid body, we take a graduated
cylinder. Fill the cylinder partly with water. Note the reading of the lower level of
water(say x₁ cc ). Now tie the given solid with a thin string and lower it gently into the  cylinder so  that the solid is completely immersed in water. The level of water is rises again.
Note the new reading of the water level raised (say x₂cc).
Since the body displaces water equal to its volume , Hence the volume of
Solid body = second reading – first reading
Thus , volume of solid = (x₂ - x₁) cubic centimeters.

To find the density of an irregular shaped body insoluble in water.

Density: The density of a substance is defined as its mass per unit volume 
Density is a scalar quantity and represented by the letter ‘d ’. If the mass of a body be M gms, and the volume of the body is V cubic cms, then
                                               d = M/V. Its unit is gm per cm³. SI unit is kg /m³.
To find the density of an irregular body , first find the mass of  the body by common  balance . Now find the volume of the body by the following steps.
To find the volume of an irregular shape of solid body, we take a graduated
cylinder. Fill the cylinder partly with water. Note the reading of the lower level of
water(say x₁ cc ). Now tie the given solid with a thin string and lower it gently into the cylinder so that the solid is completely immersed in water. The level of water is rises again.
Note the new reading of the water level raised (say x₂cc).
Since the body displaces water equal to its volume , Hence the volume of
Solid body = second reading – first reading
Thus , volume of solid = (x₂ - x₁) cubic centimeters.
Dividing Mass of the body by volume we get the density of the body.

Measurement of volume of a regular shaped body is determined 

To find the volume of a regular shaped body its dimensions such as length, breadth, height, radius etc, are measured . Then use the following relations:

Volume of cuboid = length x breadth x height
Volume of cube = (side)³
Volume of sphere =4 / 3 π (radius)³

METHOD OF MEASUREMENT OF DIFFERENT METHOD OF MEASUREMENT OF DIFFERENT PHYSICAL QUANTITIES

Method for the measurement of length with the help of ordinary scale.

Ordinary scale is a device used to measure the length of an object. 
Ordinary scale is generally made up by wood, metal or plastic. It is graduated in centimeters, millimeters. 1 centimeter is divided into 10 equal parts, each part is 1 millimeter.  
To measure the length of a line say AB, we place the scale in such a way that it remains perpendicular to the line AB. Now note the reading of the starting point and the end point B from the scale.
Then, Length of line AB = Reading of end B – Reading of end A
As  per example: Let the starting point A of the line AB is at 2 cm, coincide with the scale. If the end point B of the line does not coincide exactly with the graduation of the scale, the reading has to be taken by eye approximation method. While taking the reading  eye should be placed directly above the point B. Let the end B coincide with the scale at 6.5 cm .
 Therefore length of the line AB = 6.5cm -2cm = 4 .5 cm.

Method for the measurement of mass with the help of a common balance

Common balance is an instrument used to measure the mass of a body. 
By common balance we find the mass of a body by comparing its mass with some known standard weights. Generally we put the body on the left pan of the balance whose mass is to be determine and the standard weights are placed on the right pan. When the beam of the balance becomes horizontal then the mass of the body is equal to the standard weight. 

Method for the measurement of mass with the help of a spring balance

Spring balance is a type of balance used to measure the weight of a body.
It consists of a spring kept in a metal tube. It is partially exposed in front of the metal tube. The upper end of the spring is rigidly fixed. The lower end of the spring is attached with a metal rod. One hook is attached with the lower end of the metal rod. The body whose weight is to be determined is hanged from this hook. A pointer attached to the spring moves on a graduated scale (usually in grams or kilograms and grams ). The position of the pointer indicates the weight of the body.  

Choosing correct units and Dimension of Physical quantity

Explain  the reason of using different smaller and larger units for measuring a particular quantity.

To measure a particular quantity we use both smaller and larger units as per  requirement. For example. To measure the length of a room , we use metre(m) to measure the distance between two cities we use kilomete(km). For the measurement of the distance of a star from the earth the commonly used unit is light year. Because kilometer is considered to be a very small unit in this case.

To measure the length of a very small quantity we consider smaller unit of lengths as centimetre, millimeter, micron etc. For example to measure the thickness (or diameter) of a wire, we use centimetre or millimeters. In this case unit taken as metre is absurd.    If the thickness of  a paper measured in millimeter(mm) is 1 mm, then expressed in metre is 0.001 m, which look odd.
Therefore we should carefully examine that what unit we have to take for the measurement of a thing . If we chose a thing to measure we should take its standard unit.

Dimension of a physical quantity
Having defined the units of physical quantities, we now briefly mention the concept of dimensions of other physical quantities.
The dimension of a physical quantity is represents the powers to which the fundamental units have raised in order to obtain the derived units of the physical quantity.
The dimensions of length, mass and time are expressed in L, M and T’ respectively. Dimensions generally represents the nature of the units only. It does not indicate the magnitude of the units.

Discussion : Speed has the derived units –cm/sec., km/hr., mi/hr. etc. The most  common feature in them is that they all are  derived by dividing a unit of length by a unit of time. So the dimension of speed will be L/T or  LT ^-1    where ‘L’ stands for length and ‘T’ stands for time. Similarly different units of acceleration e.g ., cm/sec², ft/sec², mi/hr² etc. represents a unit of length divided by square of unit of time. Hence its dimension will be L/T² or L/T ^-2.
Following the same reasoning ,force which is the product of mass(M) and
aceleration (LT ^-2), has the dimension MLT ^-2.

 Measuring Instruments

 As the measurement of length, volume, mass and time  was thoroughly taken into consideration in the previous article, we shall not go through it any more.

In this article we shall rather present a brief description of some appliances for measurement of length which enables greater accuracy to be obtained than is possible by mere eye-estimation.

 To measure the different physical quantities, the commonly used measuring devices are the following.
1.    Ordinary scale (metre scale) use to measure the length of an object.

                                                            
2.     Common balance - it is used to measure the mass of a body.

                                                                            
3.     Spring balance – it is used to measure the weight of a body.

                                                              
4.     Measuring cylinder – it is used to measure the volume of a body a liquid.
        It is also used to measure the volume of a solid by displacement method.

                                                                   
5.    Clock – it is used to measure the time.

                                                               
6.    Stop watch – it is used to measure a time interval between two events such as                  race, sports , football etc.

                                                                

System of Units

 System of Units

A complete sets of units, both fundamental and derived, for all physical quantities is called a system of units. There are now mainly three systems
in common use, each of which derives its name from the initial letters of the fundamental units upon which it is based. These are:

(1 C.G.S. system, having centimetre, gram and second a fundamental units .
(2) M.K.S system, in which fundamental units are metre, kilogram and second.
(3) F.P.S system, based on foot,pound and second as fundamental units.

A fourth system of unit, namely S.I., (systeme internationale) is introduced in 1960, is described in the appendix.

The first two namely C.G.S. and  M.K.S. systems are also called metric system
and obviously metric standards of length and mass are used in them.

The F.P.S on the other hand based on the British standards.

The metric system has a definite advantage over the F.P.S. system calculations
are made easier , since the various multiples and submultiples of unit are
related by simple power of 10 .

On the other hand the F.P.S system has however , no such advantage .The
relation between the various subdivisions of a unit are rather obscure and inconvenient , such as 1 foot =12 inches ,1 yard =3 feet, 1 mile=1760 yds.
Even an inch is divided into 8ths, 16ths, 64ths to measure very small lengths.
Units of volumes of liquids.

The unit of volume of liquids, through derived ones, should be mentioned
especially, since these have different names. Thus , in metric system unit of volume is litre which is defined as the volume of 1 kg of water, at normal atmospheric pressur and the temperature of its maximum density (at 4^°C).

 Standard.

A question still remains weather there is a unique standard  for a particular  fundamental quantity . Unfortunately, the answer is ‘no’. World  is still divided into two major portions using two different standards for each of length and mass.
     In metric  system the standard of length is taken as the distance between two fine lines engraved on a platinum-irridium bar kept at International Bureau of Weight and Measures in Paris maintained at  0^°C and called International Proto-type Metre.

Defination of Metre: A metre is defined as 1,553,164.1 times the waves length of the red line in the spectrum of cadmium.

Defination of Kilogram : International Proto-type Kilogram is the standard of mass in the metric system and  is defined as the mass of a platinum-irridium cylinder kept together with Proto-type metre  at Serves near Paris ,and the copies being distributed all over the world .It was also intended to be the mass of 1000 cc. of water at its maximum density.

 Defination of second : The standard of time called mean solar second (second) is the same in both systems and is defined as 1/86400 of the average length of a solar day (mean solar day) throughout the year. This definition of a second , although 
Satisfactory for our daily routine, fails to satisfy modern scientist since the mean solar day varies from year to year and century to century.
Hence, in 1946, International Bureau of Weights and Measures defined the second as the time in which a cesium atom(which has only one isotope) undergoes  9,192,631,770 internal vibrations.

There are also some bigger units of length they are  namely

1. Kilometer(km)             2. Light year             3. Astronomical unit(AU)

1 kilomatre is equal to 1000 metre
i.e 1 kg = 1000 m or(10³m)

2. 1 Light year is the distance traveled by light in Vaccum in one year.
     1 Light year = Speed of light x 1 year
                           = 3x10³m/s x 1 year
                           = 3x10³m/s x (365x24x60x60)s
                           =9.46x10¹² km
3. Astronomical unit(AU) : It is defined as the distance of the earth from the
     sun.
        1 A.U =1.499x 10 metre.

Smaller units of length . There are some smaller units of length they are
                                             namely, (SI unit of length is metre)

     1 metre = 100 cm =1/100m
     1 metre = 1000mm=1/1000m
     1 metre = 1000000 micron  or 1 micron =10^-6 m
    1 Nanometre =10^-9m