Unit and Dimension

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Dimensional formulae & SI unit of angular momentum L= Dimensional formulae & SI unit of area A= Dimensional formulae & SI unit of density = Dimensional formulae & SI unit of gravitational constant G= Dimensional formulae SI unit of pressure p= Dimensional formulae SI unit of acceleration a= Dimensional formulae & SI unit of magnetic potential V= Dimensional formulae & SI unit of resistance R= Dimensional formulae & SI unit of permittivity = Dimensional formulae SI unit of resistivity = Dimensional formulae & SI unit of stress S= Dimensional formulae & SI unit of magnetic field B= Dimensional formulae & SI unit of co-efficient of viscosity = Dimensional formulae & SI unit of electric potential gradient K= Dimensional formulae & SI unit of thermal conductivity K= Dimensional formulae & SI unit of electric dipole moment P= Dimensional formulae & SI unit of magnetic dipole moment M= Dimensional formulae & SI unit of electric field E= Dimensional formulae & SI unit of specific heat capacity C= Dimensional formulae & SI unit of permeability = Dimensional formulae & SI unit of Planck's constant h= Dimensional formulae & SI unit of heat Q= Dimensional formulae & SI unit of conductivity = Dimensional formulae & SI unit of wavelength = Dimensional formulae & SI unit of torque =

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Dimensional formulae & SI unit of inductance L= Dimensional formulae & SI unit of capacitance C= Dimensional formulae & SI unit of electric potential V= Dimensional formulae & SI unit of electric flux = Dimensional formulae & SI unit of electromotive force emf = Dimensional formulae & SI unit of momentum p= Dimensional formulae & SI unit of velocity v= Dimensional formulae & SI unit of energy E= Dimensional formulae & SI unit of work W= Dimensional formulae & SI unit of power P= Dimensional formulae & SI unit of force F= Dimensional formulae & SI unit of surface tension T= Dimensional formulae & SI unit of time t= Dimensional formulae & SI unit of mass m= Dimensional formulae & SI unit of length L= Dimensional formulae & SI unit of angular frequency = Dimensional formulae & SI unit of angular velocity = Dimensional formulae & SI unit of angular acceleration = Conversion from inch into millimetre 1 = 25.4 Conversion from inch into centimetres 1 = 2.54 Conversion from inch into metre 1= Conversion from feet into metre 1 = 0.3048 Conversion from yards into metre 1 = 0.9144 Conversion from mile into metre 1 = 1609.344 Conversion from mile into kilometre 1 = 1.609344 Conversion from square in into centimetre 1 = 6.4516 Conversion from square in into metre 1= Conversion from square feet into metre 1= Conversion from square yard into metre 1 = 0.8361 Conversion from square yard into kilometre 1 = 2.58999 Conversion from square mile into hectare 1 = 258.999 Conversion from acres into metre 1 = 4046.856

Conversion from acres into hectare 1 = 0.40469 Conversion from cubic inch into centimetre 1 = 16.3871 Conversion from cubic inch into litre 1 = 0.016387 Conversion from cubic inch into metre 1= Conversion from cubic feet into metre 1= Conversion from cubic feet into litre 1 = 0.028317 Conversion from cubic yard into metre 1 = 0.7646 Conversion from lb into grams 1 = 453.60 Conversion from tonne into kilogram 1 = 1000 Conversion from ton into lb 1 = 2240 Conversion from feet/second into centimetre/second 1 = 30.48 Conversion from feet/second into metre/second 1 = 0.3048 Conversion from mile/hours into kilometre/hours 1 = 1.609344 Conversion from litre into metre 1 = 10 - 3 Conversion from gallon into metre 1= Conversion gallon into litre 1 = 4.560 Conversion from miles/hours into metre per second 1 = 0.48 Conversion from kilometre/hours into metre per second 1 = 0.28 Conversion from Ib into kilogram 1 = 0.454 Conversion from gram centimetre-3 into kilogram metre-3 1= Conversion from Ib/inch3 into Kilogram 1= Conversion from dyne into newton 1 = 10- 5 Conversion from kilogram force into newton 1 = 9.80 Conversion from kilowatt hours into joule 1= Conversion from Cal into j 1= Conversion from hp into w 1 = 4.186 Conversion from mm Hg into Pa 1 = 746 Conversion from atms into pa 1 = 133.322 Conversion from Ao into m 1= Conversion from micron into μ 1 = 10- 6 Conversion from hp into kw 1 = 0.7457 Conversion from Ibf into kgf 1 = 0.45359 Conversion from kw into w 1 = 1000 Conversion hp into kw 1 = 0.746 Conversion from 0F into 0C 1 = 0.55 Conversion from 0C into 0F 1 = 1.88 Dimensional formulae & SI unit of volume V=

Dimensional formulae & SI unit of moment of intertia l= Dimensional formulae & SI unit of young's modulus Y= Dimensional formulae & SI unit of frequency = Dimensional formulae & SI unit of magnetic flux = SI Units (a) Time-second(s); (b) Length-metre (m); (c) Mass-kilogram (kg); (d) Amount of substance–mole (mol); (e) Temperature-Kelvin (K); (f) Electric Current – ampere (A); (g) Luminous Intensity – Candela (cd) Uses of dimensional analysis (a) To check the accuracy of a given relation (b) To derive a relative between different physical quantities (c) To convert a physical quantity from one system to another system

Absolute in each measurement Mean absolute Fractional Percentage Combination of error

Uses of dimensional analysis. Dimensional analysis is very simple method for convert the one system of units into another system of units. And we can check the correctness of the equations. We can show the relations between physical phenomenal quantitatively. Dimension of capacitana C is [M-1 L-2 T4 A2] Dimension of charge q is [A2 T2] SI Units

The SI system (International System of Units) is the modern metric system of measurement and the dominant system of international commerce and trade. SI units are gradually replacing Imperial and USCS units. The SI is maintained by the International Bureau of Weights and Measures (BIPM, for Bureau International des Poids et Mesures) in Paris. The SI system is founded on the SI Base units The core of the SI system is a short list of base units defined in an absolute way without referring to any other units. The base units are consistent with the part of the metric system called the MKS system. The International System of Units (SI) is founded on seven base units. Quantity

Name of Unit

Symbol

Length

meter

m

Mass

kilogram

kg

Time

second

s

Electrical current

ampere

A

Thermodynamic temperature

Kelvin

K

Luminous intensity

candela

cd

Amount of substance

mole

mol

Significant Figures Every measurement involves errors. Thus, the result of measurement should be reported in a way that indicates the precision of measurement. Normally, the reported result of measurement is a number that includes all digits in the number that are known reliably plus the first digit that is uncertain. The reliable digits plus the first uncertain digit are known as significant digits or significant figures. If we say the period of oscillation of a simple pendulum is 1.62 s, the digits 1 and 6 are reliable and certain, while the digit 2 is uncertain. Thus, the measured value has three significant figures. The length of an object reported after measurement to be 287.5 cm has four significant figures, the digits 2, 8, 7 are certain while the digit 5 is uncertain. Clearly, reporting the result of measurement that includes more digits than the significant digits is superfluous and also misleading since it would give a wrong idea about the precision of measurement. The rules for determining the number of significant figures can be understood from the following examples. Significant figures indicate, as

already mentioned, the precision of measurement which depends on the least count of the measuring instrument. A choice of change of different units does not change the number of significant digits or figures in a measurement. This important remark makes most of the following observations clear: (1) For example, the length 2.308 cm has four significant figures. But in different units, the same value can be written as 0.02308 m or 23.08mm or 23080 μm. All these numbers have the same number of significant figures (digits 2, 3, 0, 8), namely four. This shows that the location of decimal point is of no consequence in determining the number of significant figures. The example gives the following rules: 1. All the non-zero digits are significant. 2. All the zeros between two non-zero digits are significant, no matter where the decimal point is, if at all. 3. If the number is less than 1, the zero(s) on the right of decimal point but to the left of the first non-zero digit are not significant. [In 0.00 2308, the underlined zeroes are not significant]. 4. The terminal or trailing zero(s) in a number without a decimal point are not significant. [Thus 123 m = 12300 cm = 123000 mm has three significant figures, the trailing zero(s) being not significant.] However, you can also see the next observation. 5. The trailing zero(s) in a number with a decimal point are significant. [The numbers 3.500 or 0.06900 have four significant figures each.] (2) There can be some confusion regarding the trailing zero(s). Suppose a length is reported to be 4.700 m. It is evident that the zeroes here are meant to convey the precision of measurement and are, therefore, significant. [If these were not, it would be superfluous to write them explicitly, the reported measurement would have been simply 4.7 m]. Now suppose we change units, then 4.700 m = 470.0 cm = 4700 mm = 0.004700 km Since the last number has trailing zero(s) in a number with no decimal, we would conclude erroneously from observation (1) above that the number has two significant figures, while in fact, it has four significant figures and a mere change of units cannot change the number of significant figures. (3) To remove such ambiguities in determining the number of significant figures, the best way is to report every measurement in scientific notation (in the power of 10). In this notation, every number is expressed as a 10b, where ‘a’ is a number between 1 and 10, and b is any positive or negative exponent (or power) of 10. It is often customary to write the decimal after the first digit. Now the confusion mentioned in above part disappears: 4.700 m = 4.700 102 cm = 4.700 103 mm = 4.700 10-3 km. The power of 10 is irrelevant to the determination of significant figures. However, all zeroes appearing in the base number in the scientific notation are significant. Each number in this case has four significant figures. Thus, in the scientific notation, no confusion arises about the trailing zero(s) in the base number a. They are always significant. (4) The scientific notation is ideal for reporting measurement. But if this is not adopted, we use the rules adopted in the preceding example: For a number greater than 1, without any decimal, the trailing zero(s) are not significant. For a number with a decimal, the trailing zero(s) are significant. (5) The digit 0 conventionally put on the left of a decimal for a number less than 1 (like 0.1250) is never significant. However, the zeroes at the end of such number are significant in a measurement. (6) The multiplying or dividing factors which are neither rounded numbers nor numbers representing measured values are exact and have infinite number of significant digits. Rules for Arithmetic Operations with Significant Figures 1. In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures. 2. In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places Rounding off the Uncertain Digits If the first non-significant figure is a 5 followed by other non-zero digits, round up the last significant figure (away from zero). For example, 1.2459 as the result of a calculation or measurement that only allows for 3 significant figures should be written 1.25. If the first non-significant figure is a 5 not followed by any other digits or followed only by zeros, rounding requires a tie-breaking rule. For example, to round 1.25 to 2 significant figures: • Round half up (also known as "5/4") rounds up to 1.3. This is the default rounding method implied in many disciplines if not specified. • Round half to even, which rounds to the nearest even number, rounds down to 1.2 in this case. The same strategy applied to 1.35 would instead round up to 1.4. Replace non-significant figures in front of the decimal by zeros. Least Count

Minimum measurement that can be made by a measuring device is known as 'LEAST COUNT'. Least count (vernier callipers) = minimum measurement on main scale / total number of divisions on vernier scale . Least count (screw gauge) = minimum measurement on main scale / total number of divisions on circular scale Solid CO2

Solid CO2 is also called Dry Ice. ​

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