Category: Notes

Significant Figures and Rounding off The Digits Physics Notes

Significant Figures:
The significant figures express the accuracy with which the physical quantity may be expressed. They are the digits which give us useful information about the accuracy of measurement.

The greater the number of significant figures obtained when making a measurement, more accurate is the measurement, conversely, a measurement made to only few significant figure is not a very accurate one. For example, a recorded figure of 5.32 means the quantity can be relied on as accurate to three significant figures and a figure of 5.321 is said to be accurate to four significant number.

The following rules have been setup for determining the number of significant figures :
1. All non-zero digits are significant. 243.48 contains five significant figures.

2. All zeros occuring between two non-zero digits are significant.

3. All zeros to the right of a decimal point and to the left of a non-zero digit are never significant 0.00678 contains three significant figures. The single zero conventionally placed to the left of the decimal point in such an expression is also never significant.

4. (a) All zeros to the right of a decimal point are significant if they are not followed by a non-zero digit. For example 30.00 contains four significant figures.
(b) All zeros to the right of the last non-zero digit after the decimal point are significant. For Example 0.054300 contains five significant figures.

5. (a) All zeros to the right of the last (rightmost) non-zero digit are not significant. Ex. 3030 contains three significant figures.
(b) All zeros to the right of the last non-zero digit are significant, if they come from a measurement.

Suppose that the distance between two objects is measured to be 3030 m. Then 3030 m contains four significant figures.

Change of units does not change the number of significant figures in a measurement.
For example, the length x = 2.308 cm has four siginificant digits. In different units, the same length can be written as x = 23.08 mm: x = 0.00002308 km. All these numbers have the same number of significant figures namely four, the digits 2, 3, 0 and 8.

Significant figures in addition and subtraction:
The accuracy of a sum or a difference is limited to the accuracy of the least accurate observation in the addition and subtraction.

Rule: Do not retain a greater number of decimal places in a result computed from addition and subtraction than in observation; which has the fewest decimal places.

Illustration: Add and substract 428.5 and 17.23 with due regards to significant figures.
We have 428.5 + 17.23 = 445.73 and 428.5-17.23 = 411.27
But in physics, the sum and difference taken in this manner are discouraged. In fact, in the data 428.5, we have assumed zero to be in second place after decimal. The data 428.5 might have been written to first decimal only because of the inability of the instrument to measure it to the further accuracy. Therefore the choice of zero only in the second decimal place of data is not justified.

To add or subtract data in such a situation there are two methods:
1. By rounding off the answer: The data 428.5 is the weakest link as its value is known upto first decimal only. Therefore the answer should also be retained only up to first decimal place.
Sum = 428.5 +17.23 ⇒ 445.73
Difference = 428.5 -17.23 ⇒ 411.27

As said earlier, in case the second decimal is occupied by 5 or more than 5. The number in first decimal is increased by 1. On the other hand if the second decimal is occupied by a number less than 5. it is ignored.

Rounding off the result of the above sum and difference to first decimal, we have correct sum = 445.7 and correct difference = 411.3

2. By rounding off the other data: The result can also be obtained by rounding off the other data in accordance with the data. Which is the weakest link. The data 17.23 should be rounded off to 17.2 (3 in second decimal place is ignored) and the added to or substracted from 428.5. Thus we have:
correct sum ⇒ 428.5 + 17.2 ⇒ 445.7 and
correct difference ⇒ 428.5 -17.2 ⇒ 411.3

Significant figures in multiplication and division: The following rule applies for multiplication and division:

Rule: The least number of significant figure in any number of the problem determines the number of significant figures in the answers. This means you must know that to recognise significant figures in order to use this rule.

Rounding Off the Digits:
Rounding off a number is done to obtain its value with a definite number of significant figures. For this following are the rules:

1. If the digit to drop is less than 5, then the preceding digit is not changed.
   For e.g., 1.24 is rounded off to 1.2.
2. If the digit to drop is greater than 5, than the preceding digit is raised by 1.
   For e.g., 19.48 is rounded off to 19.5.
3. If the digit to drop is 5 and the preceding digit is even, then it is not changed.
   For e.g., 1.25 is rounded off to 1.2.
4. If the digit to drop is 5 and the preceding digit is odd, then it is increased by 1.
   For e.g., 3.35 is rounded off to 3.4.

Physics Notes

Absolute Error, Relative Error, Percentage Error and Combination of Errors Physics Notes

Absolute error: Absolute error in the measurement of a physical quantity is the magnitude of the difference between the true value and the measured value of the quantity.

Let a physical quantity can be measured n times.
Let the measured value be a₁, a₂, a₃, ………….a_n the arithmetic mean of these values is:
a_m = \(\frac{a_{1}+a_{2}+a_{3} \ldots a_{n}}{n}\)
Usually am is taken as the true value of the quantity, if the same is unknown otherwise by definition, absolute errors in the measured value of the quantity are

Absolute errors may be positive in certain cases and negative in other cases.

Mean absolute error: It is the arithmetic mean of the magnitude of absolute errors in all the measurements of the quantity it is represented by Aa. Thus,

Hence the final result of the measurement may be written as a = am ± Δ\(\bar{a}\).
This implies that any measurement of the quantity is likely to lie between (am+Δ\(\bar{a}\)) and (am – Δ\(\bar{a}\)).

Relative error: The relative error or fractional error of measurement is defined as the ratio of mean absolute error to the mean or value of the quantity measured. Thus,
Relative error = \(\frac{\text { Mean absolute error }}{\text { Mean value }}=\frac{\Delta \bar{a}}{a_{m}}\)

Percentage error: When the relative/fractional error is expressed in term of percentage, we call it percentage error. Thus,
Percentage error = \(\frac{\Delta \bar{a}}{a_{m}}\) × 100%

Combination of Errors:
Now, we will study how errors get combined while performing mathematical operations such as addition, subtraction, multiplication and division.
1. Error in Addition of Quantities
Let x = a + b
Let Δa = absolute error in measurements of a
Δb = absolute error in measurement of b
Δx = absolute error in addition of quantities
So, x ± Δx = (a ± Δa) + (b ± Δb)
or x ± Δx = (a + b) ± Δa ± Δb
or x ± Δx = x ± Δa ± Δb
or ±Δx = ± Δa ± Δb
Here, Δx can have four possible values:
(+Δa + Δb), (+Δa – Δb), (-Δa + Δb), (-Δa – Δb)
Maximum possible error in x Δx = ±(Δa + Δb)

2. Error in Difference of Quantities
Let x = a – b
Let Δa = absolute error in a
Δb = absolute error in b
Δx = absolute error in x
x ± Δx = (a ± Δ a) – (d ± Δ b)
or, x ± Δx = (a – d) ± Δa + Δd
or, x±Δx = x±Δa + Δb
or ±Δx = ±Δa + Δb
Here, Δx can have four possible values:
(+Δa – Δb), (-Δa + Δb), (-Δa – Δb), (+Δa + Δb)

Maximum absolute error indifference of quantities
Δx = ± (Δa + Δb)

3. Error in Relation of Multiplication of Physical Quantities
Let x = a x b
Let Δa = absolute error in measurements of a
Δb = absolute error in measurements of b
Δx = absolute error in the product of a and b
x ± Δx = (a ± Δa) x (b ± Δb)

The values of both \(\frac{\Delta a}{a}\) and \(\frac{\Delta b}{b}\) is very small. So, their product will be very very small. Hence, it can be neglected.

4. Error in Relation of Physical Quantities
Let x = \(\frac{a}{b}\)
Let Δa = absolute error in a
Δb = absolute error in b

Δx = absolute error in \(\frac{a}{b}\)

The values of both \(\frac{\Delta a}{a}\) and \(\frac{\Delta b}{b}\) is very small. So, the value of their product will be very small and it can be neglected.

5. Error Due to the Power of Physical Quantities

Physics Notes

Accuracy and Errors in Measurement Physics Notes

Accuracy and Errors in Measurement:
The measuring process is essentially a process of comparison. To measure any physical quantity, we compare it with a standard (unit) of that quantity. No measurement is perfect as the errors involved in the process cannot be removed completely. Hence, in spite of our best effort, the measured value of a quantity is always somewhat different from its actual value, or true value.

Measurement error: The measurement error is defined as the difference between the true or the actual value and the measured value

i. e., the error is quantity = (True value – measurement value) of the quantity.

Types of errors in measurement:
The errors may arise from the different sources and are usually classified into the following types. These types are:
1. Systematic errors
2. Random errors
3. Gross errors

Their types are explained below in detail.
(A) Systematic errors: Systematic errors are those which occur according to a definite pattern. These errors affect the measurement alike i. e., in the same way. The causes of systematic errors are known. Therefore, such errors can be minimized.

Some of the sources of systematic errors are:
1. Instrumental errors: These errors mainly arise due to the three reasons:
(a) Inherent shortcomings of the instrument: Such types of errors are inbuilt in the instruments because of their mechanical structure. They are due to the manufacturing, calibration or operation of the device. These errors may cause the error to read too low or too high.

For example: If the instrument uses the weak spring then it gives the high value of measuring quantity. The error occurs in the instrument because of the friction or hysteresis loss.

(b) Misuse of the instrument: The error occurs in the instrument because of the fault of the operator. A good instrument used in an unintelligent way may give an enormous result.

For example: The misuse of the instrument may cause the failure to adjust the zero of instruments, poor initial adjustment, using leads of high resistance. These improper practices may not cause permanent damage to the instrument, but all the same, they cause errors.

(c) Loading effect: It is the most common type of error which is caused by the instrument in the measurement work. For example, when the voltmeter is connected to the high resistance circuit it gives a misleading reading, and when it is connected to the low resistance circuit, it gives the dependable reading. This means the voltmeter has a loading effect on the circuit.

2. Natural errors: These errors are due to the external conditions of the measuring devices. Such types of errors mainly occur due to the effect of temperature, humidity, dust, vibration or because of the magnetic or electrostatic field. The corrective measures employed to eliminate or to reduce these undesirable effects are:
The arrangement should be made to keep the conditions as constant as pcoiible.
Using the equipment which is free from these effects.
By using the techniques which eliminate the effect of these disturbances.
By applying the computed corrections.

3. Observation error: Such type of errors are due to the wrong observation of the reading. There are many sources of observational error. For example, the pointer of a voltmeter reset slightly above the surface of the scale. Thus, an error occurs unless the line of vision of the observer is exactly above the pointer. To minimise the parallax error highly accurate meters are provided with mirrored scales.

(B) Random errors: These errors are due to the unknown causes and are sometimes termed as chance errors. In an experiment, even the same person repeating an observation may get different reading every time. For example, measuring diameter of a wire with a screw gauge, one may get different readings in different observations. It may happen due to many reasons. For example due to non-uniform area of cross-section of the wire at different places, the screw might have been tightened unevenly in different observation, etc. In such a case, it may not be possible to indicate which observation is most accurate. However, if we repeat the observation a number of times, the arithmetical mean of all the reading is found to be most accurate or very close to the most accurate reading for that observation. That is why, for an experiment it is recommended to repeat an observation a number of times and then to take their arithmetical mean.

If a₁, a₂, a₃………., a_n are the n different readings in an experiment, their arithmetic mean is given by.

(C) Gross errors: This error occurs because of human mistakes. For example consider the person using the instrument takes the wrong reading, or they can record the incorrect data. Such type of error comes under the gross error. The gross error can only be avoided by taking the reading carefully.

Example: The experimenter reads the reading 31.5°C as while the actual reading is 21.5°C. This happens because of the oversights. The experimenter takes the wrong reading and because of which the error occurs in measurement.

Such type of errors are very common in measurement. The complete elimination of such type of errors is not possible. Some of the gross errors are easily detected by the experimenter but some of them are difficult to find out.

Two methods can be used to remove the gross error:

1. The reading should be taken out very carefully.
2. Two or more readings should be taken of the measurement quantity. The readings are taken by the different experimenter and at a different point to remove the errors.

Physics Notes

Least Count of Vernier Callipers and Screw Gauge Physics Notes

Least count of vernier callipers and screw gauge:
(A) Vernier callipers: It is a precision instrument that can be used to measure internal and external distances accurately.

Construction of vernier callipers:
1. Adjacent figure: A and B represents side jaws. They are used to measure the external diameter or width of an object. Here, A is a fixed Jaw and Bis a movable jaw. C and D represent inside jaws. They are used to measure the internal diameter of an object. Here, C is a fixed jaw and D is a movable jaw.

Vernier Callipers

2. Main scale: The main scale consists of a metalic steel strip graduated with the value of one division on it equal to 1 mm. It is generally 15 cm to 20 cm long. It carries the inner and outer measuring jaws. When the two jaws are in contact, the zero of the main scale and zero of the vernier scale should coincide. If both the zeros do not coinside, there will be a positive or a negative zero error.

3. Vernier scale: Vernier scale is a small movable scale which can slide along the main scale. It has 10 divisions marked on it, such that the total length of 10 divisions is equal to 9 mm. In other words, 10 vernier scale divisions coincide with nine main scale divisions.

Least count: Least count refers to the smallest distance that can be measured using an instrument. It indicates the degree of precision of an instrument.

The least count as the name suggests is the finest measurement you can take with the help of that vernier calliper. The least count (LC) of vernier scale is given as:
Least count = \(\frac{\text { Least count of main scale }}{\text { Number of divisions on vernier scale }}\)

Least count of the main scale: The main scale is callibrated in millimetres. To get the least count of the main scale, count the number of divisions on the main scale in 1 cm of it. Divide 1 cm into that much number of divisions; the value obtained is the least count 0 the mains scale in cm. For example, If there are 10 divisions is 1 cm of the main scale, its least count.
= \(\frac{1}{10}\) = 0.1 cm

Number of divisions on vernier scale: Count the number of divisions on the vernier scale. Use a magnifying glass if necessary. In most vernier caliper, the vernier scale has 10 divisions.
Thus, least count of vernier calliper
= \(\frac{0.1}{10}\) = 0.01 cm
Since the least count of the vernier calliper is 0.01 cm, it can be said that when measuring with the help of this vernier calliper, you can get an accuracy of 0.01 cm. They are extensively used to measure the internal and external diameters of tubes as well as dimensions of many more objects.

(B) The screw gauge: The screw gauge is an instrument used for measuring accurately the diameter of a thin wire or the thickness of a sheet of a metal. It consists of a U-shaped frame fitted with a screwed spindle which is attached to a thimble.

Screw Gauge

Parallel to the axis of the thimble, a scale graduated in mm is engraved, This is called the pitch scale. A sleeve is attached to the life head of the screw.

The head of the screw has a hatchet which avoids undue tightening of the screw. On the thimble, there is a circular scale known as the head scale which is divided into 50 or 100 equal parts.

A stud with a plane end surface calW the anvil is fixed on the ‘17’ frame exactly opposite to “the tip of the screw. When the tip of the screw is in contact with the anvil, usually, the zero of the head scale coincides with the zero of the pitch scale.

Pitch of the screw-gauge: The pitch of the screw-gauge is the distance moved by the spindle per revolution. To find out this, the distance advanced by the head scale over the pitch scale for a definite number of complete rotation of the screw is determined.
The pitch can be represented as:

Pitch of the screw = \(\frac{\text { Distance moved by screw }}{\text { No. of full rotations given }}\)…(1)

Least-count of the screw gauge:
The least count (LC) is the distance moved by the tip of the screw, when the screw is turned through 1 (one) division of the head scale.

The least count can be calculated using the formula:
Least count = \(\frac{\text { Pitch }}{\text { Total no. of divisions on the circular scale }}\) …(2)
Total no. of divisions on the circular scale
If the pitch of the screw is 1 mm and
If circular disc is divided into 100 equal parts,
Then L.C. = \(\frac{1}{100}\) = 0.01 mm = 0.001 cm

Physics Notes

Measurement of Large Distances Physics Notes

Measurement of Large Distances:
Length: It is defined as the difference between two positions taken by two events that occur instantly.
1. Parallax Method: When an object is seen by closing our right and left eye alternatively, there is a shift in the position of the object w.r.t. the background observed. This is known as parallax.

Imagine an object P placed at a distance x from our eyes. Let the line joining the object to left and right eye makes 0 angle w.r.t. each other. 0 is called parallax angle.

The distance LR is called basis.
θ = \(\frac{\text { Length of Arc }}{\text { Radius }}\)

Parallax Method
θ = \(\frac{b}{x}\) or x = \(\frac{b}{\theta}\)

2. Size of Astronomical Object: Diameter of Moon: Let Moon be the astronomical object whose diameter is to be measured. We observed Moon with the help of a telescope. Let it be observed from a place E on Earth and make an angle 0 with the two ends P and Q of moon and the point E, as shown in fig. 1.5. 0 is called the angular diameter of the Moon.

Let d be the distance of the Moon from the Earth.

Then, angular diameter, θ = \(\frac{\overline{P Q}}{d}\)
= \(\frac{\text { Length of the arc }}{\text { radius }}\)
or = \(\frac{D}{d}\)
or D = θd

3. Reflection or Echo Method: A gun is fired towards the hill and the time taken between instant of firing and hearing of echo be t.

In this time interval, sound first travels towards the hill from the place of firing and then back from the hill to the place of firing.
Let v be the speed of sound, x be the distance of hill from the place of firing the gun,
then, 2x = v × t or x = \(\frac{v t}{2}\)

Physics Notes

Uses and Limitations of Dimensional Equations Physics Notes

Uses of Dimensional Equations:
The dimensional equations have the three following uses:

1. For changing the magnitude of a physical quantity from one system of unit to another system of unit.
2. To check the accuracy of physical relation.
3. To establish a relationship i.e., formulae between different physical quantities.

1. Conversion of units of physical quantities from one system to another system: The method of dimensional analysis can be used to obtain the value of the physical quantity in some other system, when its value in one system is given.
As discussed earlier, the measurement of a physical quantity is given by:
Q = nu
If the unit of a physical quantity in a system is Ui, and the numerical value is then:
Q = n₁u₁ …(1)
Similar to the other system if the unit is u₂ and magnitude is n₂ then:
Q = n₂u₂ …(2)
From Eqs. (1) and (2)
n₁u₁ = n₂u₂ …………..(3)
If a,b,c are the dimensions of a physical quantity in mass, length and time, then:
n₁ [M₁^aL₁^bT₁^c] = n₂ [M₂^aL₂^bT₂^c]
Here M₁, L₁, T₁ and M₂, L₂, T₂ are the units of mass, length and time in the two systems, then;
n₁ = n₂\(\left[\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}\right]^{a}\left[\frac{\mathrm{L}_{1}}{\mathrm{~L}_{2}}\right]^{b}\left[\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right]^{c}\)
The equation can be used to find out the value of a physical quantity in the second or the new system, when its value in first system is known.

Limitations of Dimensional Equations:
The method of dimensional analysis provides simple and quick solutions to so many physical problems. However, it has a few limitations also:
1. This method does not enable us to determine the value of the constant of proportionality which may be a pure number or a dimensional ratio. The value of the constant has to be determined experimentally or by some other method.

2. This method can not be used to derive the relations, such as S = ut + \(\frac{1}{2}\) at , v² – u² = 2as, etc. by usual method. Such relations are called composite relations. Even while deriving such a relation in parts, it does not tell about the nature of the sign (plus or minus) connecting the various terms in relation.

3. This method can not be used to derive a relation in the cases. Where the trigonometric or exponential functions are involved.
Or
r = \(\left(\frac{M}{2 \pi N \rho}\right)^{1 / 3}\)
The value of r, so calculated is of the order of 10^-10 m.

Physics Notes

Dimensional Formulae and Dimensional Equations Physics Notes

Dimensional Formulae and Dimensional Equations:
The dimensional formula of a physical quantity may be defined as the expression that indicates which of the fundamental units of mass, length, and time enter into the derived unit of that quantity and with what powers.

For example, as deduced above [M⁰L¹T^-1] is the dimensional formula of velocity. It reveals that unit of velocity depends on [L], and [T]. It does not depend upon [M]. Further, unit of velocity varies directly as a unit of length and inversely as a unit of time.

Further if we represent velocity by [v], then [v] = [M⁰ L¹ T^-1]
Is called the dimensional formula of velocity. Thus when a physical quantity is equated to its dimensional formula, what we obtain is the dimensional equation of the physical quantity.

The dimensional formulae of some of the important physical quantities are derived below and are listed in Tables, I, II, III, and IV. The SI units of all these quantities are also given in these tables.

Table-I Dimensional formula of physical quantities from Mechanics:

Table-II Dimensional formulae of physical quantities from Electricity and Magnetism.

Table-III Dimensional formulae and SI units of some special physical quantities

Table-IV Quantities having the same dimensions:

Physics Notes

Dimensions of a Physical Quantity Physics Notes

Dimensions of a Physical Quantity:

The dimensions of a physical quantity is defined as the powers to which the fundamental quantities are raised in order to represent that physical quantity.
The seven fundamental quantities are denoted with square brackets [ ].

For example length is represnted by [L], mass by [M], the dimension of time is described as [T], electric current by [A] and so on.

Consider a physical quantity Q which depends on base quantities like mass, length, time, electric current, the amount of substance and temperature, when they are raised to power a, b, c, d, e and f.Then dimensions of physical quantity Q can be given as:

[Q] = [M^a L^b T^c A^d mol^e k^f]

It is mandatory for us to use [ ] in order to write the dimension of a physical quantity. Look out few examples given below:

1. The volume of a solid is given as the product of length, breadth, and its height. Its dimension is given as:
Volume = Length × Breadth × Height
Volume = [L] × [L] × [L] (as length, breadth 8 heights are length]
Volume = [L]³

As volume does not depend on mass and time, so the power of mass and time will be zero while expressing its dimensions.
The final dimension of volume will be [M]0{L]3|T]0
= [M⁰ L³ T⁰]

2. Velocity = \(\frac{\text { displacement }}{\text { time }}\)
v = \(\frac{\text { [L] }{\text { [T] }}\) = [M⁰ L^-1 T^-1]
Dimension of velocity are 0 in mass, 1 in length and -1 in time i. e., (0, 1, -1).

3 Acceleration = \(\frac{\text { changein velocity }}{\text { timetaken }}\)
= \(\frac{\text { displacement }}{\text { time } \times \text { time }}\)
a = \(\frac{\left[\mathrm{L}^{1}\right]}{\left[\mathrm{T}^{2}\right]}\)
Dimensions of acceleration are (0, 1, – 2).

4. Force:
F = mass × acceleration
= [M¹] × [M⁰ L¹ T^-2]
= [M¹ L¹ T^-2 ]
dimensions of force are (1, 1, – 2).
Note: In dimensional representation, the magnitudes are not considered.

Physics Notes

Rules to write name and symbol for units of S.I. system Physics Notes

Rules to write name and symbol for units of S.I. system:

Following are the most important rules of the SI regarding the writing of quantities, names and symbols of the units; they are valid in general, i. e., also for units that do not belong to the SI.

1. Symbols and prefixes are the same in all languages.

2. Symbols are written in lower case, except when the unit is derived from a proper name.


3. Symbols are never pluralized. e.g. 65 g (not: 65 gs), 15 km (not: 15 kms)

4. An oblique stroke ( / ) is always used with symbols rather than the word, “per”. For example km/h (not: km per hour). However, kilometre per hour (not: kilometre/hour), when writing units in full.

5. The units that are named after scientists, are not written with a capital letter. For example the unit of force named after Issac Newton is written as ‘newton’.

6. The symbols that are named after scientists are written with capital initial letter. For example the unit newton has symbol N.

7. Most single units will be written in one word, e.g., centimetre, millimeter, kilogram, kilowatt (not: centi-metre, kilo-gram etc.).

8. Always place the symbol behind the numeral for example 16.8 km, 650 g, 350 mL.

9. A number and a symbol should never be separated by an adjective.

Some examples of representation of the unit of measurement:

Physics Notes

Supplementary Units Physics Notes

Supplementary Units:

Definitions:
1. Radian: One radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

Plane angle dθ = \(\frac{d S}{r}\)
If dS = r, then dQ = 1 rad

2. Steradian: One steradian is the solid angle subtended at the center of a sphere, by that surface which is equal in area to the square of the radius of the sphere.

Solid angle (dΩ) = \(\frac{\text { Normal surfacearea }}{(\text { Radius })^{2}}\)
∴ Solid angle (dΩ) = \(\left(\frac{d A}{r^{2}}\right)\) steradian

If dA = r² then dΩ = 1 steradian
In case of complete surface area, the cubic angle subtained by it
Ω = \(\frac{4 \pi r^{2}}{r^{2}}\) = 4π steradian

Physics Notes

International Definitions of Fundamental Units Physics Notes

International Definitions of Fundamental Units:
1. Metre: 1 meter is defined as the distance travelled by light in vacuum in \(\frac{1}{299792458}\) of a second.

2. Kilogram: General Conference of Weights and Measures (GCWM) defined kilogram as the mass of Platinum Irridium cylinder kept at the Bureau of Weight and Measures at Sevres near Paris, France.

3. Second: One second is equal to the duration of 9,192,631,770 vibrations corresponding the transition between two hyperfine levels of Caesium 133 atom in the ground state.

4. Ampere: 1 ampere is the constant current which when maintained in each of the two straight parallel current-carrying conductors of infinite length of negligible area of cross-section and held one metre apart in vacuum produce a force of 2 × 10⁷ Nm between them.

5. Kelvin: 1 Kelvin is the fraction \(\frac{1}{273.16}\) of the thermodynamical temperature of the triple point of water.

6. Candela: One candela is that luminous intensity in a perpendicular direction of \(\frac{1}{600000}\) m² area of a black body at the freezing point of Platinum under a pressure of 101. 325 N m^-2.

7. Mole: One mole is that amount of substance that contains as many elementary entities as there are atoms in 0.012 kg of pure ₆C¹².

8. The Kelvin unit of thermodynamic temperature is the fraction \(\frac{1}{273.16}\) of the thermodynamic temperature of the triple point of water.

Physics Notes