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Units and measurements are the basis of our understanding of the physical world.
- They enable us to measure and compare physical quantities ranging from the expanse of the universe to the tiniest world of atoms.
- Units and measurements are specific magnitudes of quantities, defined by convention or law, serving as the standard for measuring the same quantities.
- Every other quantity of this type can be expressed as a multiple of the unit of measurement.
- Even though there are many physical quantities, a small number of units can be used to describe them all since they are interrelated.
- The units that measure the fundamental or base quantities are called fundamental or base units.
- All other units of measurement can be written in terms of the base units.
- The units that are used to measure derived quantities are called "derived units."
- All of these units, both the base units and the units that come from them, make up the system of units.
Read More: Units and Measurements Class 11 Important Questions
Key Terms: Units, Measurements, Length, Principle of Homogeneity, Dimensional Analysis, Dimensional Formula, Basic Unit, Supplementary Unit, Physical quantity, Derived units, Fundamental units
Physical Quantities
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The quantities by means of which laws of physics are described are known as physical quantities.
Measurable quantities constitute physical quantities. Length, mass, time, pressure, temperature, current, and resistance are therefore examples of physical quantities.
Classifications of the physical quantities:
- Fundamental quantities or base quantities: Physical quantities that are independent from one another are referred to as fundamental quantities.
- Derived quantities: All quantities that can be stated in terms of fundamental quantities are known as derived quantities.
Units and Measurements Class 11 Video Lecture
Read Also: Precision of a measurement
What are Units?
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The term "unit" refers to the reference standard that is used for measuring physical quantities.
A unit can be chosen arbitrarily but then it should be accepted internationally and should not vary from place to place.
Characteristics of the Unit:
- The unit should be a suitable size.
- The unit should have clear parameters.
- It should not be difficult to reproduce the unit in any case.
- The unit must stay the same.
- The unit's value should remain constant regardless of changes in physical variables such as temperature or pressure.
- Experimentally speaking, the unit should be comparable to other physical quantities of a corresponding kind.
Unity Types
There are two major types of units, namely:
- Fundamental Units: Fundamental units are just another name for the units that are defined for the fundamental quantities.
- Derived Units: The terms "derived units" and "basic units" refer, respectively, to the units of all other physical quantities that are derived from the fundamental units.
Read More:
| Relevant Concepts | ||
|---|---|---|
| Unit of Time | Unit of Voltage | Unit of Volume |
| Unit of Electricity | Unit of Length | Unit of Momentum |
Measurement
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Measurement is a process of determining how large or small a physical quantity is, as compared to a basic reference standard.
To express the measurement of a physical quantity, we need to know things
- The unit in which the quantity is measured.
- The magnitude of the quantity i.e. the number of times that unit is contained in the given physical quantity.
System of Units
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The system of units is a collection of linked units used in calculations. The system consists of base units representing base dimensions and derived units representing powers of base dimensions. The following system of units is discussed below.
- FPS System: In this system, a foot is a unit of length, a pound is a unit of mass, and a second is a unit of time.
- CGS System: In this system, centimeters, grams, and seconds serve as the units for length, mass, and time, respectively.
- MKS System: In this system, meters, kilograms, and seconds, respectively, serve as the units of length, mass, and time.
- The SI System: This is commonly utilized in all measures worldwide. The system is composed of two derived units and seven fundamental units.
![What are the System of Units]()
What are the System of Units?
Some of the basic units used for different parameters and measurements are tabulated below:
| Basic Units | ||
|---|---|---|
| Quantity | Unit | Symbol of the Unit |
| Length | Metre | m |
| Mass | Kilogram | kg |
| Time | Second | s |
| Temperature | Kelvin | K |
| Electric current | Ampere | A |
| Number of particles | Mole | mol |
| Luminous intensity | Candela | cd |
| Supplementary Units | ||
| Plane angle | Radian | rad |
| Solid angle | Steradian | sr |
Read Also: Fundamental and Derived Units of Measurement
Basic Unit
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The measurements that fall under Basic Units are:
- Meter (m): One meter is equal to the distance that light travels in a vacuum for a period of time equal to (1/299792458) seconds.
- One kilogramme (kg): is equal to the mass of a cylinder made of platinum and iridium that is stored at the National Bureau of Weights and Measures in Paris.
- Second (s): The definition of a second is the amount of time that it takes light with a particular wavelength, which was emitted by a cesium-133 atom, to complete 9192631770 vibrations.
- Ampere (A): An ampere is the current that, when it flows through two straight parallel conductors of infinite length and of negligible cross-section, and they are kept at a distance of one meter apart in a vacuum, it creates between them a force that is equal to two times ten-seven newtons per meter of length.
- Kelvin (K): This unit of temperature measurement is the proportion of the thermodynamic temperature that corresponds to the triple point of water.
- Candela (cd): A candela is a unit of measurement that is equal to 1/60th of the luminous intensity of one square centimeter of a perfect black body that is kept at the freezing temperature of platinum.
- Mole (mol): A mole is the amount of stuff that has the same number of elementary units as there are atoms in 0.012 kilograms of carbon-12. One mole is equal to the number of elementary units.
![What are Units and Measurements]()
What are Units and Measurements?
Check Out: Screw Gauge Measurement
Supplementary Units
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The measurements that fall under Supplementary Units include:
- Radian (rad): The radian is the angle that is subtended at the center of the circle by the arc whose length is equal to the radius of the circle.
- Degrees: One degree is equal to one-half of a radian.
- Steradian: The steradian is the solid angle subtended at the center of a sphere by a spherical surface with an area that is equal to the square of the radius.
Dimensional Formula
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The dimensional formula of every physical quantity is the formula that specifies which of the fundamental units were employed in its measurement.
The dimensional formula for a physical quantity can be represented as:
- The physical quantity's formula must be written down. It must be on the left side of the equation.
- All quantities on the formula's right-hand side must be expressed in terms of fundamental quantities such as mass, length, and time.
- Replace M, L, and T with mass, length, and time and write the terms' respective quantities.
Characteristics of Measurements
The characteristics of measurements include:
- Dimensions are independent of the unit system.
- Similar-sized quantities can be added or removed from one another.
- Dimensions can be derived from physical quantity units and vice versa.
- Two distinct quantities may share the same measurement.
- Multiplying or dividing two dimensions will result in the dimension of the third quantity.
Dimensional Analysis
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It is possible to use the dimensional formula to –
- To verify that the equation has been entered correctly.
- Change the unit of measurement for the physical quantity so that it corresponds to the new system.
- Determine the relationship between the physical quantities using deduction.
Defects of Dimensional Analysis
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Dimensionally correct equations are occasionally erroneous because they do not account for dimensionless constants, such as, integers.
- For instance, the dimensions of v2 + 2as and v2 + 5as are the same, yet they are physically incorrect.
- It does not determine if a physical quantity is vector or scalar.
- It cannot develop a relation or formula if a physical quantity is dependent on more than three dimensional elements.
- It cannot derive a formula with trigonometric, exponential, or logarithmic functions.
- It cannot derive a relation with several components in an equation.
Check Also: Lagrange Points
Units of Derived Quantities
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The units and dimensions of few derived quantities include:
| Physical Quantity | Unit | Dimensional Formula |
|---|---|---|
| Displacement | m | M0L1T0 |
| Area | m2 | M0L2T0 |
| Volume | m3 | M0L3T0 |
| Velocity | ms-1 | M0L1T-1 |
| Acceleration | ms-2 | M0L1T-2 |
| Density | Kg m-3 | M1L-3T0 |
| Momentum | Kg ms-1 | M1L1T-1 |
| Work/Energy/Heat | Joule (or) kg m2/sec2 | M1L2T-2 |
| Power | Watt(W) (or) Joule/sec | M1L2T-3 |
| Angular Velocity | rad s-1 | M0L0T-1 |
| Angular Acceleration | rad s-2 | M0L0T-2 |
| Moment of Inertia | Kg m2 | M1L2T0 |
| Force | Newton (or Kg m/sec2 | M1L1T-2 |
| Pressure | Newton/m (or) Kg m-1/sec2 | M1L-1T2 |
| Impulse | Newton sec (or) Kg m/sec | M1L1T1 |
| Inertia | Kg m2 | M1L2T0 |
| Electric Current | Ampere (or) C/sec | QT-1 |
| Resistance/Impedance | Ohm (or) Kg m2/sec C2 | ML2T-1Q-2 |
| EMF/Potential/Voltage | Volt (or) Kg m2/sec C2 | ML2T-2Q-1 |
| Permeability | Volt (or) Kg m2/ C2 | MLQ-2 |
| Permittivity | Farad/m (or) sec2C2/kgm3 | T2Q2M-1L3 |
| Frequency | Hertz (or) sec-1 | T-1 |
| Wavelength | m | L1 |
Principle of Homogeneity
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In order to follow the homogeneity of dimensions principle, each of the terms in a particular physical equation must have the same value.
Ex. s = ut + (½) at2
Dimensionally, it can be shown as:
[L] = [LT-1.T] + [LT-2. T2] [L] = [L] + [L]
Read More: Principle of Homogeneity of Dimensions: Applications & Limitations
Important Topics for JEE MainAs per JEE Main;2024 Session 1, important topics included in the chapter Units and Measurements are as follows:
|
Things to Remember
- Physical quantities are those quantities that can be used to explain the laws of physics. For instance: length, weight, and time
- Physical quantities can be classified as fundamental quantities and derived quantities.
- The unit is the reference standard that is used to measure physical quantities. There are two kinds of units: basic units and derived units.
- The SI is made up of 7 fundamental units and 2 derived units.
- Any physical quantity's dimensional formula is the formula that tells which of the basic units were used to measure that physical quantity.
- The formula for sizes is based on the principle of homogeneity.
Also Read:
Previous Year Questions
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Sample Questions
Ques. What is the difference between Ao and A.U.? (1 mark)
Ans: Distance is measured in Ao and A.U., although one Ao is equal to 10-10 meters whereas one A.U. measures 1.4961011 meters.
Ques. Define S.I. unit of solid angle. (1 mark)
Ans: The angle formed by a spherical plane with an area of one square meter in the center of a sphere with a radius of one meter is the definition of one steradian.
Ques. Convert 6.67 10-11Nm2/kg2 into CGS. (2 marks)
Ans: 6.67 10-11Nm2/kg2 = g-1cm3s-2
= 6.67*10-11kg-1m3s-2
= 6.67*10-11*103*(102 cm)3
= 6.67*10-8g-1cm3s-2
Ques. A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance? (2 marks)
Ans: The distance from the Sun to Earth is as follows:
= The velocity of light The amount of time it takes for light to travel a given distance
Given that one unit is equal to the speed of light according to the new system,
Time taken, t = 8 min 20 s = 500 s
The distance between the Sun and Earth is equal to 1,500, which is equivalent to 500 units.
Ques. A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of hair? (2 marks)
Ans: The microscope has a magnification factor of 100.
The hairs that were visible in the field of view of the microscope had an average width of 3.5 millimeters.
The true thickness of the hair is 3.5/100, which equates to 0.035 millimeters.
Ques. A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance? (2 marks)
Ans: The distance between the Sun and the Earth:
= Speed of light x time it takes for light to cover the distance
Since, in the new unit, the speed of light is equal to 1 unit,
Time taken,
t = 8 min 20 s
Which means,
= 500 s
The distance between the Sun and the Earth is 1 x 500, or 500 units.
Ques. On a 35 mm slide, the image of a house occupies 1.75 square millimeters. The slide is projected onto a screen, and the size of the house on the screen is 1.55 inches by 1.55 inches. What is the linear magnification of the projector and screen configuration? (1 mark)
Ans: Linear magnifications, ml=√m
√[(1.55/1.75)*104] = 94.11
Ques. Find the order of magnitude of a light-year. (1 mark)
Ans: 1 light year = 9.46 x 1015 m≈ 1016m
The order of magnitude of light-year is +16.
Ques. You are given a thread and a meter scale. How will you estimate the diameter of the thread? (2 marks)
Ans: Wrap the thread around a consistent, smooth rod such that the resulting coils are very close together. The length of the thread is determined using a meter scale. The relation gives the diameter of the thread.
Diameter = Length of thread/Number of turns
Ques. E, m, l and G denote energy, mass, angular momentum and gravitational constant respectively. Determine the dimensions of EL2 / m5G2. (3 marks)
Ans: E = [ML2T-2]
L = [ML2T-1]
m = [M]
G = [M-1L3T-2]
Hence, Dimensions of EL2/m5G2
[ML2T-2] [ML2T-1]2 / [M]5[M-1L3T-2]2
Thus, it is dimensionless.
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