PHYSICS CHAPTER 2 System of Units Class 11th Complete Solution
Physics
2
System of Units
NEED FOR MEASUREMENT
In physics, much importance is attached to measurements and for this reason. it is sometimes called as an exact science or the science of measurement. Lord Kelvin once remarked that:
When you can measure what you are speaking about and express it in numbers, you know WE something about it ; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind."
In making this statement, Lord Kelvin had actually highlighted the importance of having the quantitative knowledge (measurement) of a physical quantity. We know that in order to move a body, force has to be applied. The force so applied will produce some acceleration in the motion of the body. But how much acceleration will be produced in the motion of the body, can be known only if one measures the magnitude of the applied force and the mass of the body. Again, if we throw a stone along horizontal, it comes to rest after covering some distance.But how much distance the stone will cover, can be known, if one measures the initial speed of the stone, time taken by the stone to cover the distance and acceleration in the motion of the stone. Therefore, to know and understand a physical situation completely, one is likely to measure the quantities such as distance, speed, time, mass, acceleration, force, etc, which are called physical quantities
All quantities in terms of which laws of physics can be expressed and which can be measured directly or indirectly are called physical quantities.
UNITS FOR MEASUREMENT
Measurement of a physical quantity involves its comparison with a chosen standard of the same kind as the physical quantity.
The chosen standard of the sane kind taken as reference in order to measure a physical quantity is called the unit of that quantity.
The meaning of the measurement of a physical quantity is to find out the number of times its unit is contained in that physical quantity. Therefore, the process of measurement of a physical quantity involves:
i) the selection of unit and
ii) to find out the number of times that unit is contained in the physical quantity.
For example, if we are asked to measure the length of a table, the unit to be selected must be that of length. Suppose that we use metre as the unit. We place a metre rod successively along the length of the table and find out the number of times the metre rod is contained in the length of the table. Suppose that the length of the table is covered by the metre rod in three successive placings. Then, 3 is called th numerical value of the length of the table for metre as the unit of length. We may write :
Length of the table = 3 × 1 m = 3 m
It may be pointed out that it is not sufficient to say that the length of the table is 3. The unit of the physical quantity has also to be stated along with the result of the measurement. In general,
Measure of a physical quantity = numerical value of the physical quantity x size of its unit
If u is the size of the unit and n is the numerical value of the physical quantity X (the quantity to be measured) for the selected unit, then measure of the physical quantity
X = n u
FUNDAMENTAL AL AND DERIVED UNITS
FUNDAMENTAL units are those units, which can neither be derived from one another, nor can they be further resolved into any other units.
The quantities mass, length and the time are called fundamental physical quantities and their units are known as fundamental units.
For measuring mass, length and time, there are independent units such as kilogram, metre and second. For measuring other physical quantities, if a separate unit is defined for each of them, then it will become very difficult to remember all of them as they will be quite unrelated to each other. It is found that the units of the various physical quantities can be expressed in terms of the fundamental units of mass, length and time and such units are called derived units.
The units of all such physical quantities, which can be expressed in terms of the fundamental units of mass, length and time, are called derived units.
For example, the unit of area is a derived unit. The unit of area is area of a square having sides each of unit length. The unit of volume is volume of a cube having sides Watch out! each of unit length. In tact, the unit of any physical quantity can be derived from its defining equation. To explain, let us consider the defining equation of speed. We .(2.01) 1. The derived unit of a physi should not be expressed b slash (/). For example, speed of 10 second should not be expresse It is preferred to write it in inde i.e. as 10 ms-. 2. The use of index of notatic computation job quíte simple For example, if velocity of at in km h, it can be converte with great ease by the use notation. know that
Speed = Distance Covered / time taken
Therefore unit of speed = unit of distance i.e. length / unit of time
= metre / second = ms¹
The units of the physical quantities such as acceleration, momentum, force, work, etc are all derived units and they can be obtained by writing their defining equations in terms of fundamental physical quantities.
CHARACTERISTICS OF A STANDARD UNIT
In early days, people used to measure a distance or length of an object in terms of cubit length of the human arm from elbow to the tip of the middle finger),foot length of the human foot), etc. Such units for length measurement cannot be regarded as standards and hence these were discarded with the passage of time. A unit selected for measuring a physical quantity must fulfil the following requirements:
1.It should be well defined.
2.It should be of suitable size i.e. neither too large nor too small in comparison to the quantity to be measured.
3.It should be easily reproducible at all places.
4.It should not change with time and from place to place.
5.It should not change with change in its physical conditions, such as y point temperature, pressure, etc.
6.It should be easily accessible,
Keeping in view the requirements of a standard unit, the fundamental units of mass, length and time, namely kilogram, metre and second were defined and redefined as discussed in the following sections.
Unit of Mass
Mass of a body is the quantity of matter it contains.
It is an essential property of a material body and therefore for a material body, it can never be zero. It is not affected by the presence of other bodies. Further, it does not vary with change in temperature, pressure or location of the body in space. The internationally accepted unit of mass is kilogram.
The internationally accepted unit of mass is kilogram
i) Originally, kilogram was defined as the mass of one cubic decimetre of water at 4°C ERe temperature at which density of water is maximum).
ii) The General Conference of Weights and Measures defined kilogram as the mass of a platinum-iridium cylinder kept at the International Bureau of Weights and Measures at Sevres, near Paris, France.
Unit of length
Length an object may be define as the distance of separation between its two end.
Unit of time
The idea of passage of time occurred to man from the motion of the moon across the sky and the rotation of the earth about its own axis and around the sun. It is not possible to define time in absolute terms. However, according to Einstein, time is simply what a clock reads.
i) The Paris Academy of Science defined second as the time taken by a simple pendulum of one metre length to swing from one extreme position to the other
ii) At a particular time during the day, called noon, the sun is at highest point in the sky.
A solar day is defined as the time that elapses between noons of two consecutive daus and the mean solar day is the average of the solar days in one complete year.
A second, or better called a mean solar second, is 1/24×60×60 or 1/86, 400 the part of a mean solar day
However, the duration or the length or the mean solar day is different for different vears and hence even this definition of second becomes questionable in respect of itc. pect consistancy.
The units of mass and length defined above offered the following difficulties
i) It is difficult to preserve kilogram and a metre bar
ii) The difficult to produce replicas of kilogram and metre bar for their use in different countries
iii) It is also difficult to compare the replicas with the preserved kilogram and metre on atomic standard
SYSTEM OF UNITS
Following are the common system of units:
1.cgs system = This system of units was set up in France and it is based on centimetre, gram and second as the fundamental units of length, mass and time respectively. It is a metric system of units.
2.fps system= This system of units, also known as British system of units, is- based on foot, pound and second as the fundamental units of length, mass and time. It is not a metric system. Its use in scientific work is declining more and more.
3. mks system = This system was also set up in France. It makes use of metre. Kilogram and second as the fundamental units ot mass, length and time. It is also a metric system of units and closely related to the cgs system of units. In contrast to the ces and the fps systems of units, the mks System is a coherent system of unite im mechanics.
4. SI = The unit of mass, length and time can be used to obtain the units of physical quantity in mechanics only. These three fundamental units are not sufficient to oo he units of the physical quantities which figure up in different branches of physics.
The General Conference of Weights and Measures held in 1960 introduced a new logical system of units know was Systeme Internationale d' Unites. It is abbreviated as SI. It is based on the following seven basic and two supplementary units:
ADVANTAGE OF SI
1. It is a rational system of units = Si makes use of only one unit for one physical quantity. For example, for all types of energies viz mechanical, heat, electrical, etc joule is used as the unit of energy cgs and mks systems, different units are use for different types of energies. In mks system,mechanical energy is measured in ioule, heat energy in calorie and electrical energy in watt-hour. Further, in cgs anc mks systems, often absolute and gravitational units of a physical quantity are used But in SI, no such distinction is made.For example,in mks system, the absolute 1un Of force is newton and gravitational unit is kilogram force. But in SI, only newton is used as the unit of force.
2. SI is a coherent system of units = SI, all the derived units can be obtained by dividing and multiplying the basic and supplementary units and no numerical factors are involved. In case of cgs and mks systems, when the derived units are obtained by dividing or multiplying,sometimes,the numerical factors appear.
3. SI is closely related to cgs system = It is very easy to change over to cgs system from SI or vice versa
4.SI is a metric system = Like cgs and mks systems, SI is also a metric system. The multiples and multiples can be expressed as the powers of 10.
ABBREVIATIONS IN POWER OF TEN
In order to write very large and very small quantities compactly, sometimes we make use of certain prefixes.
The following table gives the prefixes, their symbols and their values expressed as powers of 10:
For example, 0-000003 s can be expressed as 3 x 10-s or 3 us. Similarly, a distance of 143,000 m can be expressed as 143 x 10 m or 143 km.
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