Measurement of physical quantities and system of Units

<–2/”>a >Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit. The result of a measurement of a physical quantity is expressed by a number (or numerical measure) accompanied by a unit.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same quantity. Any other value of that quantity can be expressed as a simple multiple of the unit of measurement. For example, length is a physical quantity.

Four different systems of units are commonly used in science and engineering. The difference among them arises from the difference in the units used to represent the three fundamental quantities, namely length (l), mass (m) and time (t).

The base units for length, mass and time in these systems were as follows :

• In CGS system they were centimetre, gram and second respectively.

• In FPS system they were foot, pound and second respectively.

• In MKS system they were metre, kilogram and second respectively

Table of Contents

SI Units

SI Base Units

Base quantity	Name	Symbol
length	meter	m
mass	kilogram	kg
time	second	s
electric current	ampere	A
thermodynamic temperature	kelvin	K
amount of substance	mole	mol
luminous intensity	candela	cd

SI Derived Units:-

area	square meter	m²
volume	cubic meter	m³
speed, velocity	meter per second	m/s
acceleration	meter per second squared	m/s²
wave number	reciprocal meter	m^-1
mass density	kilogram per cubic meter	kg/m³
specific volume	cubic meter per kilogram	m³/kg
current density	ampere per square meter	A/m²
Magnetic Field strength	ampere per meter	A/m
amount-of-substance concentration	mole per cubic meter	mol/m³
luminance	candela per square meter	cd/m²

MKS System

MKS unit of measurement is meter-kilogram-second. SI unit was derived from MKS system. In MKS system length is in meter (m), area is in square meter (m2 ), volume is in cubic meter (m3 ), time in second (s), mass is in kilogram (kg), weight (force) is in kilogram-meter per second square (kg-m/s2 ), density is in kilogram per centimeter square (kg/cm2 ), acceleration is in kilogram-meter per second square (kgm/s2 ), force(pressure) is in kilogram-force per square centimeter (kgf/cm2 ).

CGS System

The CGS system was introduced formally by the British Association for the Advancement of Science in 1874. It found almost immediate favor with working scientists, and it was the system most commonly used in scientific work for many years. Meanwhile, the further development of the metric system was based on meter and kilogram standards created and distributed in 1889 by the International Bureau of Weights and Measures (BIPM). During the 20th century, metric units based on the meter and kilogram–the MKS units–were used more and more in commercial transactions, engineering, and other practical areas.

Fundamental and derived quantities

A fundamental quantity is a quantity that cannot be defined in terms of other quantities. Examples of fundamental quantities include length, mass, time, electric current, temperature, amount of substance, and luminous intensity.

A derived quantity is a quantity that can be defined in terms of fundamental quantities. Examples of derived quantities include speed, acceleration, force, energy, power, and work.

SI units

The International System of Units (SI) is the modern form of the metric system. It is the most widely used system of units in the world. The SI system is based on seven base units: the metre, kilogram, second, ampere, kelvin, mole, and candela. All other SI units are derived from these base units.

Other systems of units

There are many other systems of units in use around the world. Some of the most common systems of units include the imperial system, the US customary system, and the CGS system.

Unit conversion

Unit conversion is the process of changing one unit of measurement to another. To convert from one unit to another, you need to know the relationship between the two units. For example, to convert from metres to kilometres, you multiply by 1000.

Accuracy and precision

Accuracy is the degree to which a measurement is close to the true value. Precision is the degree to which repeated measurements of the same quantity are close to each other.

Significant figures

Significant figures are the digits in a measurement that are known to be accurate. The number of significant figures in a measurement is determined by the uncertainty in the measurement.

Error analysis

Error analysis is the process of determining the uncertainty in a measurement. The uncertainty in a measurement is caused by a number of factors, including the instrument used to make the measurement, the operator making the measurement, and the Environment in which the measurement is made.

Dimensions and dimensional analysis

Dimensions are the properties that describe a physical quantity. For example, the dimensions of length are L, the dimensions of mass are M, and the dimensions of time are T. Dimensional analysis is a technique that can be used to check the correctness of equations and to convert between different units of measurement.

Measurement uncertainty

Measurement uncertainty is the degree to which a measurement is uncertain. The uncertainty in a measurement is caused by a number of factors, including the instrument used to make the measurement, the operator making the measurement, and the environment in which the measurement is made.

Measurement errors

Measurement errors are the differences between the true value of a quantity and the measured value. There are two types of measurement errors: random errors and systematic errors. Random errors are caused by factors that cannot be controlled, such as the operator making the measurement or the environment in which the measurement is made. Systematic errors are caused by factors that can be controlled, such as the instrument used to make the measurement.

Instrument calibration

Instrument calibration is the process of determining the accuracy of an instrument. Calibration is done by comparing the readings of the instrument to the known values of a standard.

Error propagation

Error propagation is the process of determining the uncertainty in a calculated quantity. The uncertainty in a calculated quantity is the sum of the uncertainties in the quantities that are used to calculate it.

Statistical methods in measurement

Statistical methods can be used to analyze data from measurements. Statistical methods can be used to determine the accuracy and precision of measurements, to identify outliers, and to estimate the uncertainty in a measurement.

Measurement in science and engineering

Measurement is an essential part of science and engineering. Measurements are used to collect data, to test hypotheses, and to design and build new products.

Measurement in everyday life

Measurement is used in everyday life in a variety of ways. For example, we use measurements to cook food, to measure our weight, and to measure the distance we travel.

What is a physical quantity?

A physical quantity is a property of an object or system that can be measured. Examples of physical quantities include length, mass, time, temperature, and velocity.

What is a system of units?

A system of units is a set of units of measurement that are used to quantify physical quantities. The most common system of units is the International System of Units (SI), which is based on the meter, kilogram, second, ampere, kelvin, mole, and candela.

What are the seven base units in the SI system?

The seven base units in the SI system are the meter, kilogram, second, ampere, kelvin, mole, and candela. The meter is the unit of length, the kilogram is the unit of mass, the second is the unit of time, the ampere is the unit of electric current, the kelvin is the unit of temperature, the mole is the unit of amount of substance, and the candela is the unit of luminous intensity.

What are the derived units in the SI system?

Derived units are units that are formed from the base units. For example, the unit of velocity is the meter per second, which is derived from the base units of length and time.

What are the prefixes used in the SI system?

Prefixes are used to indicate multiples or FRACTIONS of the base units. For example, the prefix kilo- means 1000, so the kilogram is 1000 grams. The prefix milli- means 0.001, so the millimeter is 0.001 meter.

What are the SI units for the following physical quantities: length, mass, time, temperature, velocity, acceleration, force, energy, power, and pressure?

The SI units for the following physical quantities are:

Length: meter (m)
Mass: kilogram (kg)
Time: second (s)
Temperature: kelvin (K)
Velocity: meter per second (m/s)
Acceleration: meter per second squared (m/s^2)
Force: newton (N)
Energy: joule (J)
Power: watt (W)
Pressure: pascal (Pa)

What is the difference between a scalar quantity and a vector quantity?

A scalar quantity is a quantity that has magnitude but no direction. Examples of scalar quantities include length, mass, and time. A vector quantity is a quantity that has both magnitude and direction. Examples of vector quantities include velocity, acceleration, and force.

What is the difference between absolute and relative measurement?

Absolute measurement is a measurement that is made with respect to a fixed standard. Relative measurement is a measurement that is made with respect to another quantity. For example, the length of a table is an absolute measurement, while the temperature of a room is a relative measurement.

What is the difference between direct and indirect measurement?

Direct measurement is a measurement that is made by comparing the quantity to be measured to a standard. Indirect measurement is a measurement that is made by calculating the quantity to be measured from other quantities that have been measured directly. For example, the length of a table can be measured directly by using a ruler, or it can be measured indirectly by using the Pythagorean theorem.

What is the difference between precision and accuracy?

Precision is a measure of how close the measurements of a quantity are to each other. Accuracy is a measure of how close the measurements of a quantity are to the true value of the quantity. For example, if you measure the length of a table three times and get the values 100 cm, 101 cm, and 102 cm, then your measurements are precise but not accurate. If you measure the length of the table three times and get the values 99 cm, 100 cm, and 101 cm, then your measurements are accurate but not precise.

What is the difference between systematic error and random error?

Systematic error is an error that is always present in a measurement. Random error is an error that is not always present in a measurement. For example, if you are measuring the length of a table with a ruler that is not perfectly straight, then you will have a systematic error in your measurements. If you are measuring the length of a table with a ruler that is perfectly straight, but you are not holding the ruler perfectly still, then you will have a random error in your measurements.

What is the difference between a significant figure and a non-significant figure?

A significant figure is a digit in a measurement that is known to be accurate. A non-significant figure is a digit

Sure, here are some MCQs without mentioning the topic of Measurement of physical quantities and system of Units:

Which of the following is not a fundamental unit in the International System of Units (SI)?
(A) Meter
(B) Kilogram
(C) Second
(D) Ampere
(E) Newton
Which of the following is the SI unit of mass?
(A) Kilogram
(B) Gram
(C) Tonne
(D) Newton
(E) Ampere
Which of the following is the SI unit of time?
(A) Second
(B) Minute
(C) Hour
(D) Day
(E) Week
Which of the following is the SI unit of length?
(A) Meter
(B) Kilometer
(C) Centimeter
(D) Millimeter
(E) Micrometer
Which of the following is the SI unit of speed?
(A) Meter per second
(B) Kilometer per hour
(C) Centimeter per second
(D) Millimeter per second
(E) Micrometer per second
Which of the following is the SI unit of acceleration?
(A) Meter per second squared
(B) Kilometer per hour squared
(C) Centimeter per second squared
(D) Millimeter per second squared
(E) Micrometer per second squared
Which of the following is the SI unit of force?
(A) Newton
(B) Kilogram-force
(C) Dyne
(D) Pound-force
(E) Slug
Which of the following is the SI unit of pressure?
(A) Pascal
(B) Bar
(C) Atmosphere
(D) Torr
(E) Millimeter of mercury
Which of the following is the SI unit of energy?
(A) Joule
(B) Calorie
(C) Kilocalorie
(D) Watt-hour
(E) Electronvolt
Which of the following is the SI unit of power?
(A) Watt
(B) Horsepower
(C) Kilowatt
(D) Megawatt
(E) Gigawatt
Which of the following is the SI unit of electric charge?
(A) Coulomb
(B) Ampere-second
(C) Farad
(D) Ohm
(E) Volt
Which of the following is the SI unit of electric current?
(A) Ampere
(B) Coulomb
(C) Farad
(D) Ohm
(E) Volt
Which of the following is the SI unit of electric potential difference?
(A) Volt
(B) Coulomb
(C) Farad
(D) Ohm
(E) Watt
Which of the following is the SI unit of resistance?
(A) Ohm
(B) Ampere
(C) Volt
(D) Watt
(E) Farad
Which of the following is the SI unit of capacitance?
(A) Farad
(B) Coulomb
(C) Volt
(D) Watt
(E) Ohm
Which of the following is the SI unit of magnetic field strength?
(A) Tesla
(B) Gauss
(C) Oersted
(D) Ampere-turn per meter
(E) Weber per meter squared
Which of the following is the SI unit of magnetic flux?
(A) Weber
(B) Tesla
(C) Gauss
(D) Ampere-turn per meter
(E) Weber per meter squared
Which of the following is the SI unit of inductance?
(A) Henry
(B) Farad
(C) Tesla
(D) Gauss
(E) Weber per meter squared
Which of the following is the SI unit of frequency?
(A) Hertz
(B) Second
(C) Minute
(D) Hour
(E) Day
Which of the following is the SI unit of temperature?
(A) Kelvin
(B) Celsius
(C) Fahrenheit
(D) Rankine
(E) Réaumur

I hope these MCQs are helpful!