0:00 complete chapter of units and measurement well I will teach you the complete concepts of units and measurement the first concept of this chapter is physical quantity anything which we can measure is called physical quantity for example we can measure temperature like 40° Centigrade so temperature is a physical quantity we can measure length of a room like 30 m so length is a physical quantity we can measure time like 5 minutes so time is a physical quantity we can measure mass of anything like 2 kg so mass is a physical
0:46 quantity secondly we know that we cannot measure happiness so it is not a physical quantity we cannot measure sadness so it is not a physical quantity therefore we say that anything which we can measure is called physical quantity remember that every physical quantity has two parts magnitude and unit now what is magnitude and unit well magnitude is a numerical value or simply a number like 40 30 10 Etc while unit is used to measure any physical
1:32 quantity for example let I write 10 RS we can see that 10 is a magnitude and R is a unit this unit of R tells us about the time therefore remember that magnitude is a numerical value and unit is used to highlight the respective physical quantity now we will learn types of units remember that there are two types of units the first one is base units and the second one is derived units firstly what are base units well a set of seven fundamental units and a system of measurement is
2:19 called base units the seven base units are second meter kilogram Kelvin mole m air and candila noted down that second is represented by S meter is represented by m kilogram is represented by kg Kelvin is represented by K mole is represented by m o mole ampere is represented by a and candila is represented by CD here let me teach you my personal trick to remember these seven best units I say SC KK MMS here s stands for ampere C stands
3:08 for candila K stands for kilogram this K stands for Kelvin m stands for meter this m stands for mole and this s stands for second this using my personal trick we can easily remember the seven bestas quantities now what are derived units well those units which are derived by multiplication or division of the base units are called derived units for example consider meter and meter now I multiply them I get me squared we know that it is a unit of area we know that this meter and this
3:56 meter is a base unit this me squared is a derived unit because it is derived from multiplication of two base units secondly consider this meter and second now I divide them I get meter per squared it is a unit of speed we know that meter and speed both are base units well this meter per second is a derived unit because it is derived from division of two base units just remember that derived units are those units which are derived from base units now we will learn SI units we know
4:42 that SI unit stands for system the international units in the past there was a big problem while dealing with units for example in the Europe Mass was measured in pound while in Asia like Pakistan and India Mass was measured and S it was a problem I mean two different units were used for the same physical quantity Mass not to solve this problem of different units International System of Units is introduced which we call SI units the main purpose of SI units was that all units can be easily
5:29 communicated internationally let me repeat it the main purpose of SI units was that all units can be easily communicated internationally now what is SI units well the seven base units that have been agreed upon by International agreement is called SI units we already know the trick SC KK MMS where a stands for ampere C stands for candila K stands for Kelvin K stands for kg m stands for meter this m stands for mole and S stands for
6:15 second these are the seven SI units hence noted down this list of SI units now we will learn scientific notation firstly let me ask you an important question why we study scientific notation well to save space and to save time we study scientific notation for example the mass of the Moon is 7 into 10 ra to^ 22 kg it is a very big number if we write it it will be 70 up to 270 it is too big number no to save space and to save time we use scientific
7:01 notation we write it and the scientific notation as 7 into 10 ra to the^ 22 kg secondly the diameter of an atomic nucleus is 1 into 10 ra to the power -4 M it is a very small number if we write it it is like 0.00 up to 140 it is too small number now to save space and to save time we use scientific notation to write it 1 into 10 ra to the^ -4 M just remember that we use scientific notation to save space and
7:48 time now we will learn writing scientific notation let consider this number firstly we spot the leading digit here the leading digit is seven there is no decimal point present in this number I put decimal point at the end now listen carefully if I move the decimal point to the left the exponent are power of the 10th is positive here I move the decimal point to the left 1 2 and three I leave the living digit 7 and I put decimal point after 8 I write
8:34 7245 into 10 I have moved the decimal point three times to the left I write positive3 I write positive3 as exponent so I get 7.24 into 10 rest to the^ 3 this is called scentific notation secondly consider this number number we can see that the leading digit is three there is no decimal point present in this number I put decimal point at the end now I move the decimal point to the right 1 2 3 and four I put the decimal point after the leading
9:20 digit I write three here all the digits are zero remember that we do not write them we have moved the decimal point four times I write + 4 as an exponent so I get 3 into 10 ra to the^ 4 this is called scientific notation thirdly consider this number here the decimal point is already present I move it to the left 1 and two I put it after the leading digit I write 4. 863 into 10 I have moved two
10:06 times the decimal point to the left I write to SN exponent I get 4. add 63 into 10 ra the^ 2 this is called scientific notation now consider this number remember that zero cannot be a leading digit let let me repeat this important Point remember that Zer cannot be a leading digit so here the leading digit is three now listen carefully if you move decimal point to the right the exponent will always be negative here I move this decimal point to the right 1 2 3 4 5 I put this
10:56 decimal point after the leading digit I write 3.12 into 10 I have moved the decimal point to the right five times I write Min - 5 so I get 3.12 into 10 ra to the^ - 5 this is called scientific notation therefore using this simple method we can easily convert any big or small number to a scientific notation hence noted down now we will learn significant figures well I teach this easy analy to master significant figure let consider this hungry man we
11:44 know that this man needs some sort of food because food is important certain and reliable source to kill his hunger secondly let consider that he adds some sort of fruit to his menu here let me ask you is fruit that much important to kill his hunger the answer is no it is not that much important but we cannot ignore its importance I mean fruit is necessary similarly let consider this table let the length of this table is 25.1 CM here before the decimal point there
12:30 are two digits they are certain digits and reliable well after the decimal point there is only one digit it is not that much important like fruit but it is necessary I mean we cannot ignore its importance thus we say that there are total three important digits and 25. 1 cm or we say that there are three significant figures in the length of this table remember that this length of the table contains certain and necessary digits therefore we Define significant
13:17 figure as the certain and necessary digits in any measurement is called significant figure let me repeat it the certain and necessary digits in any measurement is called significant figures hence noted down this fundamental concept of significant figures which a lot of students are not understanding now I will teach you super easy trick to find significant figure in any measurement we know that there are two types of numbers non-decimal numbers and decimal numbers and non decimal numbers to find significant figure always remember this
14:04 St go from first nonzero digit to the last nonzero digit for example consider these numbers in this number the first nonzero digit is five and the last nonzero digit is two so all these digits are significant figure I count them 1 2 3 4 5 6 th there are total six significant figures present in eight secondly in this number the first nonzero digit is two and the last nonzero digit is three so I go from 2 to
14:52 three 1 2 3 th there are total three significant figures present in it thirdly in this number the first non zero digit is four and the last nonzero digit is 1 I go from four to 1 1 2 3 4 so there are total four significant figures present in it while in case of decimal numbers we say that to find significant figures go from nonzero digit to the last for example consider these numbers and the first number the first nonzero
15:39 digit is five I go from five to the last 1 2 3 4 hence there are five significant figures present in this number in case of second number the first nonzero digit is seven I go from seven to the last last I count them 1 2 3 4 5 6 so there are six significant figures present in it in case of third number we can see that the First on zero digit is four I go from four to the last I count them 1 2 3 4 so there are four significant figure present in
16:26 it th using this trick we can easily find significant figure in any measurement if you want to learn more about significant figures watch our lecture and its link is given in the description now we will learn the important concept of accuracy and precision accuracy means how close a measurement is to the actual value for example consider this man let the actual height of this man is 3 m here are these three students I ask them to find the height of this man let the first student measure that the height of this man is 4
17:13 M let the second student measured that the height of this man is 2 m while the third student measure that the height of this man is 3 m now listen carefully there are three different Valu in this measurement the two values are totally wrong but one value is correct so we say that this is accurate measurement or it has high accuracy it is because this third value of the measurement is intersecting the actual value just remember that even if one value and a measurement is matching the actual value
17:59 we say that it is accurate or it has high accuracy on the other hand Precision means how two or more values in a measurement are close to each other for example consider this man from the previous example let the actual height of this man is 3 m now I ask these three more students to measure the height of this man let the first student measure that it is 2.5 M the second student measure it it is 2.4 M and the third student measure it 2.6 M here let me ask you is this
18:48 measurement accurate or it has high accuracy the answer is no it has low accuracy or it is not accurate because the values in the measurement do not match the actual value hence we say that it has low accuracy but here this 2.5 m is close to 2.4 M and this 2.4 m is close to 2.6 M these measured values are close to each other hence this measurement has high Precision let me repeat it these measured values are close to each other hence this measurement has high
19:34 Precision therefore we say that this measurement has low accuracy but High Precision hence noted down these important Concepts now I will teach you some questions based on the concept of accuracy and precision let consider that a skill measures the mass of an apple as constantly is 0.5 kg less than the actual mass which option is correct well the scale is constantly measuring 0.5 kg 0.5 kg and 0.5 kg less than so this measurement has high Precision because all these values are
20:20 close to each other secondly the skill is measuring the mass of an apple less than the ual value so it is not accurate or we say that it has low accuracy does the correct option is C precise but not accurate secondly consider this question the mass of a bag is 10.5 kg a student measured it as 10.5 kg 10.6 kg and 9.5 kg firstly this is accurate measurement Because the actual value 10.5 kg is
21:06 matching the measured value 10.5 kg hence this measurement is accurate or it has high accuracy secondly 10.5 kg is nearer to 10.6 kg but 10.6 kg is away from 9.5 kg the three measured values are not close to each other hence it is not precise or it has low Precision th the correct option is accurate but not precise hence noted down these important questions now I will teach you the super easy concept of dimensional formula it is super easy let consider
21:54 these important base quantities like Mass length time and current we know that the SI unit of mass is kg de of length is meter dat of time is second and that of current is ampere the dimensional symbol of mass is M length is L time is T and current is a using these dimensional symbols we can easily find dimensional formula of any quantity for example example find the dimensional formula of velocity acceleration and force well we know that velocity is equal to displacement upon time now the
22:43 dimensional symbol of displacement or length is L and that of time is T I write L upon T r² bracket l n t ra to the^ minus1 square bracket closed also we can write square bracket M to the^ 0 into L into T the^ minus1 square bracket closed here this m rest to the power 0 means that the dimensional formula has no Mass thus this is the dimensional formula of velocity secondly we know that acceleration is equal to change in
23:29 velocity upon time we already learned that velocity is equal to displacement Upon Time upon this time I write the dimensional symbol of displacement is L that of time is T and that of time is again T I get square bracket Ln T ^ minus 2 square bracket does this is the dimensional formula of acceleration thirdly in case of force we know that force is equal to mass into acceleration the dimensional symbol of mass is M we already calculated the dimensional formula of
24:16 acceleration which is L into T to the^ minus 2 I get square braet m into L into T ^ - 2 square braet this is the dimensional formula of force noted down all these dimensional formula because we will use them in the next slide now consider this question find the dimensional formula of pressure stress and modulus of elasticity well we know that pressure is equal to force upon area our pressure is equal to force upon area is equal to length into breadth we know that the
25:02 dimensional formula of force is M into L into T ra to the^ minus 2 upon the dimensional symbol of length is L and the dimensional symbol of breadth is also L now this L and this l cancel out I get square bracket M into L ra to the^ -1 into T ra to the^ - to square bracket th this is the dimensional formula of pressure secondly in case of stress we know that it is equal to force upon area we have already calculated the dimensional formula Force upon area which is square braet m into L ra to
25:50 the^ minus1 and t^ - 2 square bracket thus this is the dimensional formula of stress thirdly in case of modulus of elasticity it is equal to stress upon strand we know that strand is unitless hence elasticity is equal to stress we already calculated the dimensional formula of stress which is square bracket M into l minus1 t n - 2 square bracket th this is the dimensional formula of model of elasticity therefore remember that pressure stress and model of elasticity
26:35 have the same dimensional form hence noted down now consider this question find the dimensional formula of Worden energy torque and kinetic energy well we know that Worden is the dot product of force and distance the dimensional formula of force is M and into L and T ra to the^ minus 2 the dimensional symbol of length is l i get square bracket M into L 2 and T to^ minus 2 square bracket th this is the dimensional formula of wordan and energy remember that word done and energy are the two
27:22 faces of the same coin secondly we know that torque is the cross product of force in distance the dimensional formula of force is M into L into T ra to the^ minus 2 the dimensional symbol of length is l i get square bracket m l 2 into T ^ minus 2 squ bracket thus this is the dimensional formula of torque thirdly we know that kinetic energy is equal to to half of mv^ 2 remember that we do not consider constant like 1 by 2 and finding dimensional
28:08 formula we know that dimensional symbol of mass is M the dimensional formula of V is L into T minus 1 I take Square on 8 I get square braet m into L 2 into T to the^ - 2 square bracket th this is the dimensional formula of kinetic energy therefore remember that verden energy torque and kinetic energy all have the same dimensional formo hence noted down this easy concept of dimensional formula now we will learn measurement of length we know that there are two
28:55 methods to measure length direct method and indirect method we use direct method to measure length when both ends are approachable for example consider this pencil we can touch the end of the pencil so we use meter skill to find its length remember that the least count of a meter rule is 1 mm by least count I mean the smallest length which is measured with the instrument the second instrument is verer caliper its least count is 0.1 mm the third instrument is cre G its
29:41 least count is 0.01 mm on the other hand we used indirect method to measure the length when both ears are not approachable for example the indirect method is paralex method we use this method to find large distance between two Heaven bodies like distance between the Earth and the moon the second indirect method is reflexive method now let me teach you the important concept of paralex method firstly let me teach you that what is paralex Method consider this pencil here look at the pencil now close your left
30:27 eye next open your left eye and close your right eye then repeat this process quickly you can observe that the pencil shift from left to right and vice versa this shift is due to the distance between your two eyes we call it apparent shift or parallx method therefore we Define paralex method as the apparent shift in the position of object when viewed from different positions is called paralex method remember that paralex method is used to measure large distance for example the method is used
31:14 to measure the distance between the Earth and the moon now I will teach you how mathematically we understand paralex method let consider this circle here I draw this sector we know that this is radius R and this is Arc Length L it extends an angle Theta at the center remember that the angle Theta is always measured in radian let me repeat it the angle Theta is always measured in radian according to the equation Theta is equal to Ark length upon radius R Theta is equal to l upon R using this
32:02 equation we can easily measure large distance for example consider this numerical problem the Moon is observed from two points A and B on the earth the angle Theta subtended at the Moon by the two points of observation is 1° 54 minute the diameter of the earth is about 1.27 6 and to 10 ra to the^ 7 m find the distance of the moon from the earth well I draw a freehand diagram for it consider the Moon and the Earth let the diameter of the earth is L it subtended an angle Theta at the Moon let
32:48 the distance between the Earth and the moon is R now I write the given data the angle subed at the Moon Theta is equal to 1° 54 minute secondly the diameter of the earth L is 1 276 into 10^ 7 m we are asked to find the distance of the moon from the earth which is r and it is unknown here remember that 360° is equal to 2 pi radian 180° is equal to pi radian 1 de is = to < upon 180 radian and 1° is equal to 60
33:34 Minute we can see that the angle Theta is given in degree minutes we need to convert it to radians in the first step I will convert minute to degree the value of theta is 1° and 54 minute I convert 54 minute to degree we know that in 1° there are 60 Minute then in 54 minute there are X De after cross multiplication I get 60x is = to 54 into 1 or X is equal to 54 upon 60 our X is equal to 0.9 de thus in 54 minutes there are 0.9
34:24 de I write 1° + Plus instead of 54 minute I write 0.9 DE after addition I get Theta is equal to 1.9 de in the second step I will convert degree to radian the value of theta is 1.9 de we know that in 1° there is pi by 180 radian then in 1 9° there is pi radians after calculation I get Theta is equal to 0.332
35:10 radians this 1.9 de is equal to 0.332 radians now according to the equation Theta is equal to l by R we know that L is the diameter of the Earth Earth R is the distance between the Earth and the moon we are asked to find the distance R from the Earth to the Moon I shift R from the right hand side to the left hand side I get R is equal to l upon Theta now I put the values in this equation I write R is equal to the value of L is 1.
35:56 276 into 10 ra to the^ 7 m upon the value of theta which is 0 0332 radians after calculation I get 3.85 into 10 ra to the^ 8 m thus the distance between the Earth and the moon is 3.85 into 10^ 8 m therefore we say that paralex method is used to measure large distance hence noted down this important concept remember that I will skip some easy Concepts like measurements of time
36:42 and mass because they are super easy and you can learn them just by reading them now we will learn error in measurement remember that there is always some sort of error in measurement we cannot eliminate it completely but we can minimize its effect here you must learn that what is an error in measurement well consider this pencil let the actual value of the pencil is 5 cm now I ask you to find its length using meter scale let you measure that the length of this pencil is 4 cm
37:27 here there are two values actual length and measure length I mean actual length is 5 cm and measure length is 4 cm there is difference between actual length and measure length this difference between actual length and measure length is called an error in measurement I mean there is 1 cm error in your measurement therefore we Define an error as the difference between measured value and actual value is called an error let me repeat it the difference between measured value and actual value is
38:14 called an error this we say that there is 1 cm error in your measurement now we will learn some important types of error the first one is r error and the second one is systematic error firstly we will understand the concept of random error which a lot of students are not understanding let consider that you are writing a research paper and suddenly you hear a blast or noise due to which you do not concentrate and you make an error now this error or disturbance is caused by by external Source or noise we call this
39:01 error as random error therefore we Define random error as the uncertain disturbances occur in the experiment is called random error for example consider this thermometer let one person reads at 27.5 De centigrade and another person reads at 27.8 De Centigrade there is an error in taking reading which is called random error this random error occurs due to disturbance caused by external or unknown source now how can we eliminate random
39:48 error well by taking large number of observations and then taking their average by this way we can eliminate random error hence noted down this important type of error on the other hand the systematic error reminds me that there is error in the system consider this system Let There is a hole at the bottom here I am interested to fill this object but the waters leak out from it due to the hole at the bottom it means that there is error in the the system due to which the system cannot be filled this error in the system is
40:33 called systematic error therefore we Define systematic error as the error arises due to the incorrect caliberation of the device is called systematic error for example consider this clock that it is always 5 minute fast so every time you check the time you will get a wrong time it is because there is error in the clock which we call systematic error now how can we eliminate systematic error well the best way to eliminate systematic error is to select better instruments and improving experimental
41:21 techniques just remember that systematic error means error in the system like this clock hence noted down this important concept of systematic error now I will teach you calculation of Errors the first one is absolute error the concept of these error seems boring once I do some sort of numerical problems then you will Master them so watch it completely to learn absolute error you must learn two important terms terms measured values and True Value let I measure time like A1 A2 A3 A4 and
42:09 A5 these are called measured values now I take mean or average of these values I write a mean is equal to A1 + A2 + A3 + A4 + A5 here are total five values I divided by five now listen carefully this a mean of these values is called True Value let me repeat it this A mean of these values is called True Value just remember that true value is nothing but the mean or average of measured values here this A1 or A2 is individual
42:55 value of the measurement now what is absolute error well absolute error is equal to individual value minus True Value remember that we represent absolute error by Delta the absolute error of A1 is Del A1 is equal to A1 minus a mean the absolute error of A2 is Del A2 is equal to A2 minus a mean the absolute absolute error of A3 is D A3 is equal to A3 minus a mean and then D A4 is equal to A4 minus a mean Del A5 is equal to A5 - a mean therefore we Define
43:45 absolute error as the difference between individual value and True Value is called absolute error just remember that absolute error means when we subtract True Value from Individual value here you must learn mean absolute error by mean absolute error I mean taking average of absolute error we know that absolute error is denoted by Del all measurement is a I take its mean so this Delta a mean means mean absolute error it is equal to mod of absolute
44:30 error of A1 Plus mod of absolute error of A2 plus mod of absolute error of A3 plus mod of absolute error of A4 and plus mod of absolute error of A5 there are total five values I divide it by five th this is known as mean absolute error now the second one is relative error to learn relative error we again need to understand two terms True Value and mean absolute error we know that true value is the average or mean of all measured values and it is a mean while
45:16 mean absolute error is equal to Del a mean now listen carefully relative error is equal to mod of mean absolute error upon mod of True Value we know that mean absolute error is Del a mean I write d a is equal to d a mean upon a mean th this is the term of relative error therefore we Define relative error as the ratio of mean absolute error to the ratio of True Value is called relative error hence noted down lastly the third one is percentage
46:01 error it is super easy we Define percentage error is when relative error is represented as percentage it is called percentage error we know that relative error is equal to mod of mean absolute error upon mod of True Value here if I take percentage of this relative error it becomes percentage error so this is the equation of percentage error hence noted down all these important Concepts which I will use in the next numerical problem now let consider this numerical problem in successive measurement of period of oscillation of pendulum the
46:48 reading turn out to be 2.54 second 2.4 seconds and 2.70 seconds calculate absolute error relative error and percentage error well I write the given data A1 is equal to 2.54 seconds A2 is equal to 2.40 seconds and A3 is equal to 2.70 seconds firstly I find absolute error we know that absolute error is equal to measured value and True Value also we know that true value is equal to average of measured values a is equal to
47:34 A1 is 2.54 seconds plus A2 is 2.40 seconds plus A3 is 2.70 seconds upon there are three measured values I divide it by three after calculation I get 2.55 seconds now the absolute error of of A1 is Del A1 is equal to A1 minus a me A1 is 2.54 minus a is 2.55 I get - 0.01c the absolute error D A2 is equal to A2 minus a mean A2 is 2.40 seconds
48:24 and a is 2.55 seconds I get - 0.15 seconds the absolute error Del A3 is equal to A3 minus a mean A3 is 2.70 seconds and amine is 2.5 and amine is 2.55 seconds I get 0.15 seconds th these are the values of absolute error now I will find the mean absolute error mean absolute error Del a mean is equal to mod of D A1 Plus mod of D A2 plus mod
49:11 of D A3 upon three we already calculated the absolute error of A1 A2 and A3 remember that I take only positive values of absolute error because mean absolute error is the mod of these values I write D A1 is + 0.01 second A2 is 0.1 seconds and A3 is 0.15 seconds upon 3 after calculation I get Del a mean is equal to+ - 0.10 this mean absolute error is plusus
49:56 us 0.10 now we will calculate relative error we know that it is equal to Del a is equal to mean absolute error upon True Values we already know that mean absolute error is 0.10 while True Value is 2.5 I get 0.04 thus the relative error is 0.04 finally we will calculate percentage error percentage error is mean absolute error upon True Value and 200 the mean absolute error is 0.10 upon the true value is
50:44 2.5 into 100 after calculation I get 4% so percentage error is 4% therefore using this formula we can easily calculate absolute error mean absolute error relative error and percentage error I hope that you have mastered the chapter of units and measurement
