# Chapter 1 Class 11 Unit and Measurement Notes

In this post, we will provide you chapter 1 of physics unit and measurement notes. The notes was written by air 1. Students of class 11 or jee-neet aspirants can easily read and revise their syllabus for examination.

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## Unit

It is the smallest part of physical quantity (a quantity which is to be measured) in any system of units. Any standard unit should have the following two properties:

**(a) Invariability:** The standard unit must be invariable. Thus assuming your height as standard unit of length is not invariable because your height changes with your age.

**(b) Availability:** The standard unit should be easily made available for comparing with other quantities. Also you will not be available every where for comparison.There are different system of units as stated below:

**(i) F.P.S. system of units: **It is the British engineering system of units which uses foot as the unit of length, pound as the unit of mass and second as the unit of time.

**(ii) C.GS. system of units:** It is the Gaussian system which uses centimetre, gram and second as the units for length, mass and time respectively.

**(iii) M.K.S system of units:** In this system metre, kilogram and second are the units of length, mass and time respectively.

**(iv) International system of units (SI units): **This system of units was introduced in 1960, by the general conference of Weights and Measures and was internationally accepted. Our calculations mainly will be in this system of units. Units are divided in two groups as fundamental units and derived units.

### A. Fundamental Unit

If the unit of a physical quantity is independent of the other units, the physical quantity is said to be fundamental quantity and its unit as fundamental unit.

S. No. | Fundamental Quantity | Fundamental unit | unit symbol used |

1 | Mass | Kilogram | Kg |

2 | Length | metre | m |

3 | Time | second | s |

4 | Temperature | kelvin | K |

5 | Electric current | ampere | A |

6 | Luminous intensity | candela | cd |

7 | Amount of matter | mole | mol |

Note: (1) Unit cannot be plural e.g., writing 5 kgs is wrong, the correct is 5 kg.

(2) If the name of a unit is the name of a scientist and you are writing the complete name start from small letter, e.g., 5 ampere and if you are writing the single letter use capital letter, e.g., 5 A.

### Derived Quantity

If the unit of a physical quantity depends on the units of the fundamental quantities then the quantity is said to be dependent physical quantity (derived quantity) and its unit is dependent unit or (derived unit). e.g. unt of velocity is m/s, which depends on the unit of length and time and hence the velocity is said to be dependent quantity and its unit as derived unit.

**METRIC PREFIXES FOR POWERS OF 10:** The physical quantities whose magnitude is either too large or too small can be expressed more compactly by the use of certain prefixes as given in the table.

## Order of Magnitude

If the magnitude of a physical quantity is expressed as a\times10^{b}, where (a\le5), then the exponent b is called the order of magnitude of the physical quantity. If 5<a\le10 then the order of magnitude of the physical quantity become b+1. where b is any positive or negative exponent (or power) of 10.For example, the speed of light is given as 3.00\times10^{8}ms^{-1}.

So the order of magnitude of the speed of light is of magnitude, gives an estimate of the magnitude of the quantity. The charge on an electron is 31.6\times10^{-19}c Therefore, we can say that the charge possessed by an electron is of the order 10^{-19}Or^{15} order of magnitude is 19. The expression of a quantity as a\times10^{b} is called scientific notation.

## Accuracy, Precision of Instruments

**Accuracy: **It is a measure of how close the measured value is to the true value of the quantity. It may depend on many factors. As we reduce the errors, the measurement becomes more accurate. Let the true value of a quantity is 3.9 and its measurements taken by two boys are 3.6 and 3.8. Here 3.8 is more accurate as it is closer to the true value.

**Precision**: It tells us as to what resolution or limit, the quantity is measured. It mainly depends on least count of instrument. If we measure a certain thickness by two different devices having resolutions 0,1 cm (a metre scale) and 0.01 cm (a vernier callipers), the latter will give a measurement having more precision. Thus a value 1.56 is more precise than 1.5.

It is not necessary that a more precise value is more accurate too. Let a man measures a length of 5.65 cm by the above mentioned two devices, and obtains the values 5.5 cm and 5.34 cm respectively. Though the first value is less precise, it is more accurate as it is closer to the true value. And 5.34 cm is less accurate but more precise.

## Errors in Measurement

The difference of true value and measured value is called error in measurement. Error = Measured value – True value.

**Various Types of Error**

**(1) Systematic error:** This error occur only in one direction, ie, either positive or negative.This error arise due to following reasonsImproper designing or calibration Least count of instrument.

(i) Instrumental Errors (ii) Imperfection in experimental technique (iii) Variation in experimental condition: Like change in temperature, wind speed, humidity etc.(iv) Personal error: Error due to carelessness or casual behaviour.

**(2) Random Error: **The error which cannot be associated with any constant caused called random error. This error can be randomly have any sign i.e. positive or negative.

## Significant Figures

The number of digits in the measured value about the correctness of which we are sure plus one more digit are called significant figures.

**Rules for counting the significant figures:**

Rule 1: All non zero digits are significant. For example 12376 has 5 significant figures.

Rule II: All zeros occurring between the non zero digits are significant. For example 230089 contains six significant figures

Rule III: All zeros to the left of non zero digit and right of decimal are not significant. For example 0.0023 contains two significant figures.

Rule IV: If a number ends in zeros that are not to the right of a decimal, the zeros are not significant.For example, number of significant figures in 1500 (Two), 1.5 x 10 (Two), 1.500 x 10 (Three)1.5000 x 10 (Four)

Rule V: All zeros to the right of decimal and right of non zero are significant. Example 0.0052300 contains 5 significant.

Note:. Larger the number of significant figures obtained in measurement greater is the accuracy of the measurement.In exponential notation the numerical portion gives the number of significant figures.

## Dimensions of Physical Quantities

These are the power raised to the fundamental units to write down the unit of a physical quantity e.g., the unit of velocity is m/s. It can be also be written as ms-1.

Hence Dimension of length in velocity is=+1. Dimension of time in velocity is=-1.

The symbolic form of dimension formula for fundamental quantities are M, L, T, K, A, cd, mol for the fundamental quantities mass, length, time, temperature, current, luminous intensity and amount of matter respectively. Hence overall dimension of velocity is written as LT-1. Dimension is also represented in capital bracket. The Dimensions of velocity can also be written as [M°LT-1].

## Dimensional Analysis and it’s Application

**A. Homogeneity of dimensions in an equation:** It states that in a correct physical equation the dimensions on two sides of sign (+) (-) and (=) are same. This is called principle of homogeneity.

With the help of above statement we can check the correctness of a physical equation.

A dimensionally correct equation may be numerically incorrect, but numerically correct equation will be always dimensionally correct.

A dimensionally incorrect equation will be always incorrect equation.

Let us check the equation v=u+at. Here u is the initial velocity, v is the final velocity, a is constant acceleration and t is the time considered for motion between a segment of path.

[u] = [m/s] = [L.T^{-1}] [V] = [m/s]=[L.T^{-1}} [af] [acceleration) [time] = [LT^-2] [T] =[LT^-1]Thus, the equation is correct as the dimensions of each term are the same. So, we can say that the equation is dimensionally correct.

## Limitation of the Dimensional Method

1. If dimensions are given, physical quantity may not be unique for example, work, energy and torque all have the same dimensional formula ML^{2}T^{-2}.

2. Numerical constants cannot be deduced by the method of dimensions.

3. The method of dimensions cannot be used to derive relations other than product of power function. For example, s=ut+\frac{1}{2}at^{2} or y = Asin(wt + 5) can’t be derived by this method.

4. The method of dimensions cannot be applied to derive formula, if a physical quantity depends on more than three physical quantities because unknowns will be more than equations. However correctness can be checked.0.g~T=2\pi\sqrt{\frac{l}{mgL}} can’t be derived by dimensional analysis but its correctness can be checked.

5. Even if a physical quantity depends on three physical quantities, out of which two have same dimensions, the formula cannot be derived by theory of dimensions, e.g. the frequency of a tuning fork cannot be derived but can be checked for correctness.