This action might not be possible to undo. Are you sure you want to continue?
measuring things accurately. In India a carpenter buys wood by the cubic foot, petrol is sold by the litre gold by the gram land by the acre, vegetables by the kg and cable by the metre. In the United States, a carpenter pays for wood by the board-foot, petrol is sold by the gallon, and a jeweler sells gold by the ounce, land is sold by the acre, fruits and vegetables are sold by the pound, and electric cable is sold by the yard. uyers and sellers have always tried to cheat each other by wrongly representing the !uantity of the product e"changed. #hen the ancient $gyptians built the pyramids, they measured the stones they cut using body dimensions every worker could easily understand. Small distances were measured in digits %the width of a finger& and longer distances in cubits %the length from the tip of the elbow to the tip of the middle finger' ( cubit ) *+ digits&. ,he -omans were famous road builders and measured distances in paces %( pace ) two steps&. .rchaeologists have uncovered ancient -oman roads and found milestones marking each (/// paces %mil is 0atin for (///&. ,he 1anes were a seafaring people and interested in knowing the depth of water in shipping channels. ,hey measured soundings in fathoms %the distance from the tip of the middle finger on one hand to the tip of the middle finger on the other& so navigators could easily visuali2e how much clearance their boats would have. In $ngland distances were defined with reference to body features of the king. . yard was the circumference of his waist' an inch was the width of his thumb, and a foot the length of his foot. Scientists today prefer to use the metric system. ,he metric system did not evolve from a variety of ancient measurement systems, but was a logical, simplified system developed in $urope during the seventeenth and eighteenth centuries. ,he metric system is now the mandatory system of measurement in every country of the world e"cept the United States, 0iberia and urma %3yanmar&. In (45/, an international conference was called to standardi2e the metric system. ,he international System of Units %SI& was established in which all units of measurement are based upon seven base units6 meter %distance&, kilogram %mass&, second %time&, ampere %electrical current&, 7elvin %temperature&, mole %!uantity&, and candela %luminous intensity&. ,he metric system simplifies measurement by using a single base unit for each !uantity and by establishing decimal relationships among the various units of that same !uantity. For e"ample, the meter is the base unit of length and other necessary units are simple multiples or sub-multiples6 ,he table shows the SI prefi"es and symbols. ,hroughout this book we use the metric system of measurement.
/// /// //( /.///./// //( /.hese SI base units or commonly called metric units are6 2 .///. that is used as a standard for measurement of the same physical !uantity. units of !uantities can be e"pressed as combinations of units of other !uantities.///./// /// /// //( /./// (./// /// /// /// /// //( Prefix e"a peta tera giga mega kilo hecto deka deci centi milli micro nano pico femto atto Symbol $ 9 ./// (// (/ ( /.///.///.///.///./// (./( /./// /// /// /// //( /.///.he International System of Units %SI& defines seven fundamental units of measurement.///.///./// (. Using physical laws.( /./// (.///. : 3 k h da d c m m n p f a (/(* 4 (/5 ./// (. the other units are derived units.///. .///. (/-5 -4 (/-(* -(8 (/-(+ Unit: .ny other value of the physical !uantity can be e"pressed as a simple multiple of the unit of measurement. SI Fundamental Units . .hus only a small set of base units is re!uired.///. .//( /. defined and adopted by convention or by law. (/* ( (// -( (/-* -. Fundamental or ase Units and !eri"ed Units: .Table 1: SI Prefixes and Symbols Factor (/(+ (/ (/ (/ (/ (/ (/ (/ (/ (8 Decimal Representation (. fundamental unit of measurement is a defined unit that cannot be described as a function of other units. International System of Units .///. unit of measurement is a definite amount of a physical !uantity. <ot all !uantities re!uire a unit of their own.he International System of Units %SI& defined seven basic units of measure from which all other SI units are derived.
and r is radius. Measurement of %en$th Measurement of %ar$e !istances: Parallax Method In order to calculate how far away a star is.5/ degrees& is the length of the entire circumference divided by the radius. the paralla" shift is too small to measure. or *Cr @r. ? ) s @r. where ? is the subtended angle in radians. . . #hen the stars are very far away. 7 cd mol #rea of Science . ecause of the $arthEs revolution about the sun. In the SI System of Units.hus *C radians is e!ual to . 3 . astronomers are able to calculate the paralla" angle across the sky.ime 0ength or distance 3ass $lectric =urrent . s is arc length. >ne radian is the angle subtended at the center of a circle by an arc that is e!ual in length to the radius of the circle.emperature 0uminous Intensity . meaning that one radian is e!ual to (+/@C degrees. a solid angle %symbol6 D& is the two-dimensional angle in three-dimensional space that an object subtends at a point. the magnitude in radians of such a subtended angle is e!ual to the ratio of the arc length to the radius of the circle' that is. the radian is a pure number and the symbol AradA is usually omitted. . and when degrees are meant the symbol B is used. It is a measure of how large the object appears to an observer looking from that point.he smaller the paralla" shift.ll .s the ratio of two lengths.Measure . 3ore generally.5/ degrees. . It follows that the magnitude in radians of one complete revolution %. . y observing the distance of the shift and knowing the diameter of the $arthEs orbit. astronomers use a method called paralla". a solid angle is a dimensionless unit of measurement called a steradian %symbol6 sr&.ll 9hysics 9hysics 9hysics >ptics =hemistry Plane an$le: -adian describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc. or *C. the farther away from earth the star is.mpere 7elvin =andela 3ole Symbol s m kg .his is called paralla" shift. complete revolution is *C radians %shown here with a circle of radius one and thus circumference *C&.mount of Substance Unit Second 3eter or 3etre 7ilogram . Solid #n$le: In geometry. In the absence of any symbol radians are assumed. near stars seem to shift their position against the farther stars.his method is only accurate for stars within a few hundred light-years of $arth. .
In microbiology and biochemistry. they needed a unified system of keeping time. . biology. ut as people began to feel the need to coordinate their actions.+ H+*%+. physics. (an$e of Masses Measurement of Time Jumans have been measuring time for a relatively short period in our long history.he 1alton %symbol 1. . efore that.he desire to synchroni2e our activities came about 8. so itGs convenient to state their masses in terms of Ithousands of unified atomic mass unitsG. It is defined as (@(* %one-twelfth& of the mass of an isolated carbon-(* atom.he second %symbol6 s& is the base unit of time in the International System of Units and is also a unit of time in other systems of measurement' it is the second division of the 4 . in kilograms ) (. tome was divided only into daylight and night. many molecules have hundreds. ./(* kilogram of carbon (*. or thousands. sitting in a vault in 9aris.& " (/-*H kg.he kilogram is defined in terms of a bar of platinum-iridium alloy./// years ago as our nomadic ancestors began to settle and build civili2ations.he standard F throughout chemistry. .Measurement of &ery Small !istances: ''See power point (an$e of %en$ths Measurement of Mass Unified #tomic Mass Unit:.he number of atoms there are in a mole of an element is given by .s itGs a unit of mass.55/ 8. or 1a& is the same as the unified atomic mass unit. the mole. with days for hunting and working and nights for sleeping.he symbol amu.vogadroGs number. etc F is the unified atomic mass unit %symbol u&.he kilogram and unified atomic mass unit are related via a primary SI unit. ./// or 5. the atomic mass unit %u& has a value. . but one that is accepted for use with the SI. which is defined as the amount of substance of a system which contains as many elementary entities as there are atoms in /. It is important to recogni2e that the unified atomic mass unit is not an SI unit. so the convention is to use k1a %kilodaltons&. . of constituent atoms. which stands for atomic mass unit is defined in terms of o"ygen .
. the second has been defined to be the duration of 4(4*5. #ccuracy: . #ith the advent of atomic clocks. it became feasible to define the second based on fundamental properties of nature. the errors in e"perimental data are those that are always unknown to some e"tent and carry some amount of uncertainty.he precision of a measurement system.hour by si"ty.here may be certain fi"ed errors which will cause repeated readings to be in error by roughly some amount for some unknown reasons.herefore.ime is one of the seven fundamental physical !uantities in the International System of Units.(HH/ periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium (. Since (45H. . systematic errors may be divided into following sub-categories6 Instrumental *rrors <o apparatus can be constructed to satisfy all specifications completely. .hese errors always give a constant deviation. then it always gives the error in the reading. such as radio waves.he uncertainty may vary a great deal depending upon the circumstances of the e"periment. . thus the sunFearth motion is no longer considered a suitable basis for definition of time. . the first division by 5/ being the minute. such as velocity and acceleration.ime is used to define other !uantities. .. =locks based on this jumping within atoms can therefore provide an e"tremely precise way to count seconds. 5 . it was defined in terms of the period of the $arthEs orbit around the Sun. #ccuracy) Precision of Instruments and *rrors in Measurement *rror: $rror is the actual difference between a measured value and the known standard value. atom.here is a possibility of error due to the division of the scale not being uniform and clear.he accuracy of a measurement system is the degree of closeness of measurements of a !uantity to that !uantityEs actual value. %c& 9aralla"6 #ithout a mirror under the pointer there may be paralla" error in reading. >n the basis of the sources of errors. . . Imperfections in *xperimental Techni+ue or Procedure Following are some of the reasons of errors in results of the indicating instruments6 %a& =onstruction of the Scale6 . In other words.stronomical observations of the (4th and */th centuries revealed that the mean solar day is slowly lengthening. reasonable definition of e"perimental uncertainty may be taken as the possible value the error may have.1 (/// and (45/ the second was defined as (@+5. . %b& Fitness and Straightness of the 9ointer6 If the pointer is not fine and straight. a manufacturer always mentions the minimum possible errors in the construction of the instruments. %d& $fficiency or skill of the observer 6 $rror in the reading is largely dependent upon the skill of the observer in reading the measurement accurately. #hen e"posed to certain fre!uencies of radiation.K// of a mean solar day.his is the reason of giving guarantees within a limit. 9recision6 . ut it is now defined more precisely in atomic terms. is the degree to which repeated measurements under unchanged conditions show the same results. Systematic *rrors . the subatomic particles called electrons that orbit an atomEs nucleus will AjumpA back and forth between energy states. etween . etween (45/ and (45H.hese are called systematic errors and are inherent errors of instruments or methods.
ll measuring instruments used in physics have a least count. .bsolute $rror6 .. y definition6 Pa() am F a( Pa*) am F a* L am F an 3ean . we do not consider the N. %east Count *rror . a* . :enerally./* millimeters.. .hese are random errors and their magnitudes are not constant.N .Personal *rrors It is due to the variation in final adjustment of the measuring apparatus. these errors may be minimi2ed by taking the average of a large number of readings.an are the individual values then6 . meter rulerEs least count is /. (elati"e *rror or Fractional *rror: .he error varies from person to person.fter corrections have been applied for all the parameters whose influences are known. 9ersons performing the e"periment have no control over the origin of these errors.bsolute error is defined as the magnitude of difference between the actual and the individual values of any !uantity in !uestion. 9ercentage $rror )mean absolute value@mean value " (//) Pamean@am"(// 6 .. L.sign in its value.bsolute $rror ) Pamean) ∑∆a / n i =1 i i =n <ote6 #hile calculating absolute mean value.rithmetic mean am ) Ma(Na*Na. Say we measure any given !uantity for n number of times and a(. .anO@n am) ∑n i= 1 i =n ai 1efinition of absolute error6 . a vernier caliper a least count of /. the law of probability may be applied.//(g.he A0east =ountA of any measuring e!uipment is the smallest !uantity that can be measured accurately using that instrument. .( centimeter' an electronic scale may have a least count of /. #bsolute *rror) (elati"e *rror and Percenta$e *rror . In the case of random errors.hese errors may be either positive or negative.his is defined as the ration of mean absolute error to the mean value of the measured !uantity6 Qa )mean absolute value@mean value ) Pamean@am Percenta$e *rror: It is the relative error measured in percentage.he magnitude of the difference between the individual measurements and the true value of the !uantity is called the absolute error of the measurement. there is some deviation left..hus 0east =ount indicates the degree of accuracy of measurement that can be achieved by the measuring instrument. . . (andom *rrors . a..
. the 2eroes are not necessarily significant6 (4/ miles may be * or . %K& .*/ g has * significant figures. depending on whether the number of significant figures is .he number (.he potential ambiguity in the last rule can be avoided by the use of standard e"ponential. *xact . or Ascientific./5 S (/K calories %. students in a class.he number of significant figures in a result is simply the number of figures that are known with some degree of reliability.. the number of significant figures is clearly indicated by the number of numerical figures in the EdigitE term as shown by these e"amples.K g has K significant figures./(* g has * significant figures.ll non2ero digits are significant6 (. .*.he number (.A notation. . $"act numbers can be considered to have an infinite number of significant 7 .* is said to have . we would write 8/../5// S (/K calories %8 significant figures& y writing a number in scientific notation./*. significant figures.Si$nificant Fi$ures .5// calories as6 8. significant figures. %8& #hen a number ends in 2eroes that are not to the right of a decimal point./ ml has . or 8. or 8. significant figures.railing 2eroes that are also to the right of a decimal point in a number are significant6 /. or 8 significant figures.& 0eading 2eros to the left of the first non2ero digits are not significant' such 2eroes merely indicate the position of the decimal point6 /. K. /.* g has * significant figures. 8/. there might be e"actly *. %*& Reroes between non2ero digits are significant6 (//* kg has K significant figures. (ules for decidin$ the number of si$nificant fi$ures in a measured +uantity: %(& .umber: . . significant figures. significant figures& 8.//(o = has only ( significant figure. (./H m0 has . /. ...5// calories may be . $"act numbers are often found as conversion factors or as counts of objects. K. 3ost e"act numbers are integers6 e"actly (* inches are in a foot.n e"act number is e"act if it is known with complete certainty. For e"ample.*/ is said to have K significant figures./5/ S (/K calories %K significant figures&. %.
5* N /.H5 N .K ) T ../+. the last remaining digit is increased by one.. %*& If the digit to be dropped is less than 8.. K./ %* significant figures& S (*. . For e"ample6 (// %assume ./.*. . For e"ample.5( ) T (*8 .he rationale for this rule is to avoid bias in rounding6 half of the time we round up. %.his rule means that if the digit to be dropped is 8 followed only by 2eroes.K is rounded to (*. half the time we round down. however. %(& In addition and subtraction.H.+/// which should be rounded to .. the result is rounded off so that it has the same number of digits as the measurement having the fewest decimal places %counting from left to right&. but left as it is if even. For e"ample. %8 significant figures& ) (*. the last remaining digit is increased by one if it is odd. (ules for mathematical operations: In carrying out calculations. *.5 is rounded to (.+ %* significant figures&./ N *H.. . the result is rounded off to the last common digit occurring furthest to the right in all components. the general rule is that the accuracy of a calculated result is limited by the least accurate measurement involved in the calculation. . (ules for roundin$ off numbers %(& If the digit to be dropped is greater than 8. For e"ample... . and if any digit following it is not 2ero.5(K ) T (/K..(8 . %K& If the digit to be dropped is 8 and is followed only by 2eroes. the number of apparent significant figures in any e"act number can be ignored as a limiting factor in determining the number of significant figures in the result of a calculation. significant figures& N *. (*. significant figures&. For e"ample. ((.8 is rounded to (*. the last retained digit is increased by one.8( is rounded to (.hus. Sample problems on si$nificant fi$ures (. N K.5K.4/H N **5. the last remaining digit is left as it is. (*. which should be rounded to (*K %.figures. <ote. (*.5. . %*& In multiplication and division.5/ %K significant figures& ) .H.(4.. .8 is rounded to (*.& If the digit to be dropped is 8. the result should be rounded off so as to have the same number of significant figures as in the component with the least number of significant figures.nother way to state this rule is as follows6 in addition and subtraction. the result is always rounded to the even digit.(/4 ) T 8 . For e"ample. that it is possible two numbers have no common digits %significant figures in the same digit column&.*.5K. (*.
#hat is the average of /../ @ 8.. 4.. /.885 S %K/ . (/.K ) *5+.8 ) 8. *. /.(H/K.(H(8T .. (*. ) T %8. ./ 5//.// " (/8 .+H %8.(4.*. that is not unambiguous./.5( ) (.* (*8 .8. and /.K " (/* . then the result should be (.H " (/* /.H. . which rounds to /../* ) T /.(H*/.*.. /. /.*. 5.(H(.H /. K..nswer key to sample problems on significant figures (.g.(H(../* S *. because there is no decimal point.(H((+.*.. and /. N K..8& ) K (/.(H(8T #hat is the standard deviation of the numbers in !uestion ((T (. /.8 " (/*./* ) ((K. /..8K (/K.his answer assumes that K8 has two significant figures' however.(. a count&.8 " (/* ) T %:ive the e"act numerical result.*.8 ) T 5//.he average of these numbers is calculated to be /. and then e"press that result to the correct number of significant figures&.8&. ) T /.(8 .5(K ) *+5.* S *H.(/4 ) (*4 %assuming that (*8 has .885 S %K/ .. 5. ) /. #hat is the standard deviation of the numbers in !uestion ((T 9 ../* S *. If K8 is an e"act number %e. significant figures&.* S *H./ N *H./ @ 8.(H(* . H.//. K8 S .5. H. +.(H/H. ((.//.4/H N **5.(H*/. ) (.*. ((.// ) T #hat is the average of /.(H/K./+. *.8& ) T K8 S .(H/H.( .H5 N . 4.. +. . *. . (*. and because it is not e"pressed in scientific notation. 8.// ) (.*.8&.5* N /.
M0O. ..O. . .he converse.(H(* instead of the more accurate /. the diameter of a proton.ime intervals.4e-//K 3icrosoft $"cel gives /. we are not using those symbols to represent an actual variableXwe will not assign any particular values or use any specific units for those symbols. Instead. all timestamps and time intervals have dimension of time. lengths. #hen we talk about a !uantityGs physical dimension.+/ " (/-K %e"pressed in scientific notation&. Wou will never be able to assign a value to a time coordinate using units of lengthXlength and time are fundamentally distinct and ine!uivalent physical dimensions. So6 all distances./4K5.// " (/8 . we will henceforth set aside symbols in s!uare brackets whenever making a statement about physical dimensions.. .hese results should be rounded to /. 9hysical dimension is an inherent and unvarying property for a given !uantity. and so forth.. $"amples6 1imensional formula of volume M3/0. Jewlett-9ackard 8/: calculator gives 5.. or . .hey are all measured in different ways.U*O *xamples: V . we need to define an appropriate unit for the measurement.. which is 5. and then e"press that result to the correct number of significant figures&. V . and widths have dimension of length.. (. . .H4588(5.0.hey are the powers %or e"ponents& to which the units of base !uantities are raised for representing a derived unit of that !uantity. M.H4588(5. Ythis !uantity has physical dimension 0Z. .he physical dimension of a !uantity is determined by how we measure that !uantityXand to do that./4K5K//////////// . heights. using symbols such as 0 for length. when we write.he result that you get in calculating the standard deviation of these numbers depends on the number of digits retained in the intermediate digits of the calculation. 0.8 " (/* ) T %:ive the e"act numerical result. if you used /.///5.U(O 1imensional formula of acceleration M3/0. all share the common feature of having a physical dimension of time. or any other measurement characteri2ing duration. For e"ample.o make this distinction e"plicit../O 1imensional formula of velocity M3/0.+/.he 3athworks 3. however.(.(H((+ as the mean in the standard deviation calculation that would be wrong %donEt round intermediate results or you will introduce propagated error into your calculations&.hen. given !uantity can only ever have one specific physical dimension. !imensions of Physical -uantities !imensions: 9hysical dimension is a generic description of the kind of !uantity being measured. the distance from the $arth to the 3oon./4e-/K . is not true6 different physical !uantities can have the same physical dimension. and might have their values assigned using different units. std function gives 5. the symbol 0 really just means YLhaving a length unitZ. and the thickness of a piece of paper all involve a measurement of a length.he height of a building.H4588(5. for time... click here to send your answer and to receive an answer key and e"planation by email. timestamps. 1oing the math right is the first step. #e can make different 10 . .///5. but they all share the common feature of being a kind of length. . of some kind.
he following !uantities are e"amples of such !uantities. . refractive inde". solid angle. M0O. $"6 1imensional formula of Force F ) M3[(0[(. and nautical miles are all very different units. ^uestion6 Jow can you derive 1imensional formula of a derived physical !uantity.O Substitute these dimensional formulas in above e!uation we get p _M3[(0[(.[\-*]O . angular displacement. V ^uantities having no units. ii& Using the units of the derived physical !uantity. $"6 1imensional e!uation of $nergy is $ ) M3[(0[*. -elative permittivity. . furlongs. strain. they must all have the same physical dimension. but no dimensions6 9lane angle. V ^uantities having units. $&. V ^uantities having both units ` dimensions6 .hese physical !uantities possess units but they does not possess dimensional formulas. specific gravity. can not possess dimensions6 . For e"ample6 meters. -elative permeability. coefficient of friction. 11 .[\*]O #e get F _ M3OM0 . e"ponential functions. !imensional Formulae and !imensional *+uations 1imensional Formula6 1imensional formula of a derived physical !uantity is the Ye"pression showing powers to which different fundamental units are raisedZ.ns6 #e can derive dimensional formula of any derived physical !uantity in two ways i& Using the formula of the physical !uantity6 $"6 let us derive dimensional formula of Force.rigonometric ratios. but the all share the common feature of being lengths. but whatever those alternative unit choices are. Force F) ma' substitute the dimensional formula of mass m _M3O ' acceleration _M0. $"6 let us derive the dimensional formula of momentum.[\-*]O 1imensional e!uation6 #hen the dimensional formula of a physical !uantity is e"pressed in the form of an e!uation by writing the physical !uantity on the left hand side and the dimensional formula on the right hand side. Unit of 3omentum % p & _ Mkg-m sec[\-(]O ' kg is unit of mass _ M3O ' is unit of length _ M0O ' sec is the unit of time _M.g.choices for the units we use %e. the SI system versus the ritish $ngineering system.ll these !uantities neither possess units nor dimensional formulas.[\-*]O' F _M3[(0[(. then the resultant e!uation is called 1imensional e!uation. inches.[\-*]O . logarithmic functions.[\-(]O. . 9oissonGs ratio.
subtracted%-& or compared %).J.cceleration. aelocity. Solution6 t = 2π l g 1imension of 0.-* " . 0 ut6 velocity " time ) 0. $"ample6 =heck the correctness of the relation t = 2π l where l is length and t is time period of g a simple pendulum' g is acceleration due to gravity. $nergy etc. nor does it tell us whether the constant (@* is correct or not.J.ll three terms must have the same dimensions. the given relation is correct. It is e"tremely useful to perform a dimensional analysis on any doubtful e!uation according to the following rules6 .nalysis >nly !uantities with like dimensions may be added%N&.S ) t ) . . %(& . 0 ) 0. Force. even though their units 12 .c&. $!uations in physics must be dimensionally consistent. .he e!uation contains three terms6 s.S ) -.-( " .wo !uantities can only be e!ual if they are of the same dimension.S ) L LT −2 %*C is a constant&' T 2 =T 1imensionally.J. s ) ut N (@* at*. . Speed.ll three terms have units of length and hence this e!uation is dimensionally valid.. Chec.* ) 0 . 1imension of -.in$ the !imensional Consistency of *+uations ased on the principle of homogeneity of dimensions only that formula is correct in which the dimensions of the various terms on one side of the relation are e!ual to the respective dimensions of these terms on the other side of the relation. It is perfectly valid to write (* inches ) ( foot because both of them are lengths. >f course this does not tell us if the e!uation is physically correct. . $"ample of checking for dimensional consistency =onsider one of the e!uations of constant acceleration.1ensity. not the units. It is also possible to use dimensional analysis to suggest plausible e!uations when we know which !uantities are involved. 0. <ote that only the dimension needs to be the same. !imensional #nalysis and its #pplications 1imensional .his rule provides a powerful tool for checking whether or not e!uations are dimensionally consistent. ut and (@*at *.rea. aolume.wo !uantities can only be added or subtracted if they are of the same dimension.b.J. ) 0 (@*at* ) acceleration " time ) 0. s6 displacement ) a unit of length.S' therefore.
http6@@cbse-notes. and a.he centripetal force.. it is not valid to write " inches ) t seconds because they have different dimensions. v.html 13 . velocity %v& and radius %r& of the circle. we get F ) km(v*rU( #hich is the re!uired relation for centripetal force. >n writing the dimensions of various !uantities in %i&.U* ) 3a0b N c. 0 and . c are the powers of m. !educin$ (elationships amon$ Physical -uantities $"ample6 . b N c ) ( L%ii& From %ii&. F acting on a particle moving uniformly in a circle may depend upon the mass %m&.are different. 1erive the formula for F using the method of dimensions. r respectively.blogspot.Ub0c or 3(0(.U*O ) 3a M0. c ) ( U b ) ( U * ) U( >n putting these values in %i&. k is the dimensionless constant of proportionality.in@*/(*@/8@cbse-class-"i-physics-ch*-dimension. b. b) *.Ub >n applying the principle of homogeneity of dimensions. Solution6 0et F ) kmavbrc L %i& #here. we get a ) (.U(Ob 0c ) 3a0b. Jowever. we get M3(0(.
This action might not be possible to undo. Are you sure you want to continue?
We've moved you to where you read on your other device.
Get the full title to continue listening from where you left off, or restart the preview.