The main units used by scientists around the world were CGS, FPS, and MKS.

Systems of Unit	What each letter in the system denote
CGS	Centimeter, Gram, Second
FPS	Foot, Pound, Second
MKS	Meter, Kilogram, Second

 

 

Length measurements belong to the basic measurements. The vernier calipers, screw gauge, etc. help measure distances in small quantities in centimeter and millimeter ranges. Whereas large range distances like distances between sun and earth could be measured using a method called parallax. 

Parallax method: When we hold anything in front of our eyes and close one eye and view the object suddenly we experience a shift in its position regarding the background, this is called parallax. Here, two reference points are required. They are called the basis. If we consider the position of the earth at diametrically opposite sides of the sun to connect and become the baseline, then using the shift we could calculate the distance. This angle is tiny, it is called the parallactic angle.

\( D=\frac{b}{\theta} \)

Where D: distance between the planet or star to earth

B: distance between the points where earth appears diametrically opposite to the sun

:parallax angle which is always less than 1

To measure small distances, microscopic measurements are to be taken. Approximations of spherical properties could be used

The SI unit of length is meter, and it is represented as m. The dimensional representation is L. This length varies from the atomic distances in Fermi to mega or giga lightyears in the scale of the universe. Other length-related measurements are the fermi, astronomical unit, parsec, lightyear, etc.

Mass is a basic property, which describes the amount of matter present in any substance. 

Unified atomic mass: Unified atomic mass refers to measurements relating to atoms. It expresses the masses of atoms in the order of (1/12) of the mass of a Carbon 12 atom. Masses can be measured using mass spectrographs, common balance, etc. 

The SI unit of mass is kilogram, and it is represented as kg. The range of masses varies from the mass of an electron to the mass of the observable universe. It is dimensionally represented as M.

Time is generally measured by us using a clock. Atomic standard clock works on the vibrations of the cesium atom. They are the most accurate measures of time. Indian Standard Time is maintained by the Cesium clock placed in NPL, Delhi. 

The SI unit of time is second. It is expressed as s. It's dimensionally expressed as T. The range of values varies from the lifespan of the most unstable nuclei to the age of the universe.

These are some technical terms related to measurement. Measurement is always related to uncertainty. There will be a slight variation even in the most accurate measurements from the true value. This difference is termed an error. Precision is the limit of the measurement.
Accuracy measures how close the measured value is to the true value. For example, consider 5 to be our true value, and when we measure, we get 6, 5.1, 4, etc., and 5.1 is the most accurate value. Among the values 5.5, 5.0001 the second one is the more precise value.

Types of errors:

1. Systematic errors:

These are errors in a particular direction and occur repeatedly.

1. Instrumental errors: They are errors occurring due to the incorrect calibration, manufacture, use of instruments. If a scale is not properly calibrated or broken, or the calibrations are wrong, then there will be errors of this type.
2. Imperfection in technique: These are the errors occurring in faulty procedures. If an experiment is to be conducted in darkness, then if we measure it in light, there will be errors in our method. 
3. Personal errors: These are the errors happening for an experimenter. If measurements are taken by a person having low eyesight, then there will be issues in measurement.

2. Random errors:

These are irregular, unprecedented errors. If measurements are taken during the fluctuations of electricity, temperature and even wind, errors occur.

3. Least count error: 

The least count is the smallest measurement possible by any device. The error associated with its resolution is the least count error.

Absolute error, Relative Error, and Percentage error:

The difference between the true value and the measured value is the absolute error. Its modulus is taken. So, the difference will be positive in all cases. The average of a set of absolute errors gives the mean absolute error. The ratio of the mean absolute error to the mean error is the relative error. If it is taken in percentages, it is called percentage error.

Type of error measurement	Expression
Absolute error	\( \mid \triangle \alpha\mid = a= a - an \)
Mean absolute error	\( \sum \mid\triangle a\mid/n \)
Relative error	\( \triangle \)a mean / a mean
Percentage relative error	(\( \triangle \)a mean / a mean) *100

 

Combination of errors:

1. The error of sum or difference: When two measurements are added or subtracted, the absolute errors are always summed.
2. Errors of product or quotient: When two measurements are multiplied or divided, the relative error is the sum of relative errors. 
3. Errors in power: The error of a value raised to the power of n is found as the product of n multiplied with the errors.

The measured values are always represented in magnitude using numbers. In a number, the number of meaningful digits is called the significant figures. Some rules related to significant figures are:

• All digits other than zero are significant.
• The zeroes in between two non-zero values are significant.
• The zeroes at the end of a number without a decimal point are not significant.
• For numbers less than 1, the preceding zeros are not counted.

The power to which a measurement is raised is the order of magnitude.

There are also rules relating to rounding off like:

• If the value after the decimal point is greater than 5, one is added to the main value before the decimal.
• If it is less than 5, then the main value remains unchanged. 
• If the value is exactly 5, then if the preceding number is odd, then one is added to it and if it is even, there will be no change.

Dimensions are basically the power or the number to which the physical quantity is raised in the base units. The basic dimensions are M: mass, L: length, and T: time.

Dimensions could be combined to yield expressions connecting the base quantities about how and which quantities are involved; this is the dimensional formula.

The dimensional analysis could be used to

•  Verify equations.
• It could be used to represent relationships or derive the expressions. But it won't yield the constant terms in an expression. 
• Used to eliminate options from MCQ-type questions sometimes.

1. What are the important topics in units and measurements?

A. The SI units, Error measurements and Errors in arithmetic calculations, Significant figures, and Dimensional analysis are the important topics in this chapter.

2. What are SI Units according to NCERT Solutions for Class 11 Physics Chapter

A. The SI units are the System of Standard units which are accepted and used internationally. They are well-defined and have standard units. These include meters, kilograms, etc. There are seven basic units in this currently. All physical measurements, including the basic and derived units, could be written using these. Joule, Newton, etc. are some derived units.

3. What is the marks distribution for Class 11 Physics Chapter 2?

A. From the first section, including the three chapters from 1 to 3, 20 marks could be expected. The dimensional analysis and the rules for calculating errors and significant figures need to be focused on while studying.