Concept: Units and Measurements
A physical quantity is the property of an object that can be measured with a measuring instrument.
Examples: Length, mass, time, etc.
Types of physical quantities:
1. Fundamental quantities: These quantities do not depend on other types of physical quantities.
Examples: Length, mass, time, temperature, electric current, luminous intensity, and amount of substance.
2. Derived quantities: These physical quantities depend on the fundamental physical quantities.
Examples: Area = Length × Breadth; Density = Mass ∕ Volume.
Unit of a physical quantity:
The standard used for measuring a physical quantity is called the unit of that physical quantity.
Examples: The length of a stick is 6 centimetres. Here, length is a physical quantity, and centimetre is its unit.
- Units describe the concept of physical quantities.
- It helps us to determine the dimensions of physical quantities.
- It states if there is an error in the measurement of a given physical quantity with justification.
- It should be well defined.
- It should be universally accepted.
- It should not change with time and place.
- It should be readily available.
- We need to measure items while cooking.
- In grocery stores, we buy different things that need to be measured. Solid items like flour, rice, etc., are measured in grams or kilograms, while liquids like juice, oil, etc., are measured in millilitres or litres.
- Distance travelled is measured in kilometres and miles.
- The area of land is measured in acres, hectares, square kilometres, and yards.
- Time is important to measure as it indicates the duration of our work or any other activity.
- So, measurement of weight, volume, length, and time are part of our daily lives.
- The difference between the true and measured values is known as the error in measurement.
- For a low value of error, the measurement is more accurate.
- Errors cannot be eliminated, but they can be minimised.
- An ammeter is a measuring instrument used to measure the current in a circuit.
- The means of measuring time on the earth are not metric as our planet revolves around the Sun in 365.25 days, and we cannot turn this into a multiple of 10.
Requirements of the standard unit:
Types of units:
1. Fundamental units: The units used to measure the fundamental quantities are called fundamental units. There are seven fundamental units.
Examples: Metre, kilogram, second, ampere, candela, mole, and kelvin.
2. Derived units: The units used to measure the derived quantities are called derived units.
Examples: Watt, hertz, coulomb, dyne, etc.
System of units:
A set of fundamental and derived units is called a system of units. Following are some examples of the system of units based on the units of length, mass and time.
1. C.G.S. System:
In this system, centimetre, gram, and second are the units of length, mass, and time, respectively.
2. M.K.S. System:
In this system metre, kilogram, and second are the units of length, mass, and time, respectively.
3. F.P.S. System:
In this system, foot, pound, and second are the units of length, mass, and time, respectively.
Standard units of measurements:
Scientists worldwide have accepted a set of standard units for measurements. This system of units is called the International System of Units (SI units). In 1790, the French created a standard unit of measurement called the metric system, which is followed by the SI units.
Examples: SI unit of length is metre (m) while the unit is a kilometre (km) for large distances. 1 km = 1000 m
Few examples of fundamental units:
|Fundamental quantities||SI unit||Symbol|
|Amount of substance||mole||mol|
Few examples of derived units:
|Derived quantities||Formula||SI unit|
|Area||A = Length × Breadth||m2|
|Volume||V = Length × Breadth × Height||m3|
|Density||d = Mass ∕ Volume||Kg ∕ m3|
|Speed||v = Distance ∕ Time||m ∕ s|
|Acceleration||a = Change in velocity ∕ Time||m ∕ s2|
|Force||F = Mass × Acceleration||N ∕ kg-ms2|
|Work||W = Force × Distance||J or N×m|
Importance of measurement:
Errors in measurement:
Types of errors:
1. Instrumental errors: These errors occur due to the use of faulty instruments.
Examples: If the metre scale is not calibrated correctly, each measured value gives the same error.
2. Systemic error: These errors occur due to the defective setting in the measuring instruments. Such errors can be minimised by detecting their causes.
Examples: If the pointer of the ammeter is not pivoted precisely at the zero of the scale, it will not point to zero when no current is passing through it.
3. Random errors/Accidental errors: These errors occur due to sudden changes in the experimental conditions. These are uncontrolled errors. These errors cannot be eliminated but can be minimised.
Examples: Change in temperature or pressure, change in humidity, fluctuation in voltage, etc.
Luminous intensity: It is the quantity of visible light that is emitted in unit time per unit solid angle.
Dimension of a physical quantity: It is the number of times the fundamental units of mass, length, and time appear in the physical quantity.
Calibration: It is the process of checking and correcting the way how a measuring instrument works.
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