Unit and Measurement Notes PDF Details | |
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PDF Name | Unit and Measurement Notes PDF |

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PDF Size | 0.28 MB |

Language | English |

Category | English |

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## Unit and Measurement Notes

Hello friends, here we are going to presnet a **Unit and Measurement Notes PDF** for all of you. A unit of measurement to measure a physical quantity, we compare this quantity to a recognized, reference standard chosen at a certain, even basis. This reference standard is called standard unit and the measure of any physical quantity is expressed by writing a numerical number in front of the unit.

This is called the importance of that physical quantity. In reading the words like unit and measure, it seems that these two are the same, but there is a lot of difference between them which you can easily know through this article. For example: Suppose you go to collect a fruit (physical amount), and you take two fruits.

But to find out the value of the fruit, the seller compares it with the help of any unit (100 g, 500 g and 1 kg) and will measure it and then tell you its value. Therefore, when we compare any physical quantity with any unit, then this process is called measurement. Whereas a unit is a standard used to measure different physical quantities.

### Unit and Measurement Notes PDF

The comparison of any physical quantity with its standard unit is called measurement.

**Physical Quantities**

All the quantities in terms of which laws of physics are described, and whose measurement is necessary are called physical quantities.

**Units**

- A definite amount of a physical quantity is taken as its standard unit.
- The standard unit should be easily reproducible and internationally accepted.

**Fundamental Units**

Those physical quantities which are independent of each other are called fundamental quantities and their units are called fundamental units.

S.No. |
Fundamental Quantities |
Fundamental Units |
Symbol |
---|---|---|---|

1. |
Length | metre | m |

2. |
Mass | kilogram | kg |

3. |
Time | second | S |

4. |
Temperature | kelvin | kg |

5. |
Electric current | ampere | A |

6. |
Luminous intensity | candela | cd |

7. |
Amount of substance | mole | mol |

**Units**

The reference standard used to measure the physical quantities is called the unit.

**Properties of Unit**

- The unit should be of some suitable size
- The unit must be well-defined
- The unit should be easily reproducible in all places
- The unit must not change with time
- The unit should not change with physical conditions like temperature, pressure etc.
- The unit must be easily comparable experimentally with similar physical quantities.

**Types of Units**

**(i) Fundamental Units**

The units defined for the fundamental quantities are called fundamental units.

**(ii) Derived Units**

The units of all other physical quantities which are derived from the fundamental units are called the derived units.

**System of Units**

**(1) FPS System:** In this system, the unit of length is the foot, the unit of mass is the pound and the unit of time is second.

**(2) CGS System: **In this system, the units of length, mass and time are centimetre, gram and second, respectively.

**(3) MKS System: **In this system, the unit of length, mass and time are meters, kilograms and second, respectively.

**(4) SI System: **This system is widely used in all measurements throughout the world. The system is based on seven basic units and two supplementary units.

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 |

### Definitions of Fundamental Units

**The seven fundamental units of SI have been defined here:**

**1 Kilogram:**1 kilogram is a cylindrical prototype mass made of platinum and iridium alloys of height 39 mm and diameter 39 mm. It is a mass of 5.0188 x 1025 atoms of carbon-12.**1 Metre:**1 metre is the distance that contains 1650763.73 wavelengths of orange-red light of Kr-86.**1 Second:**1 second is the time in which a caesium atom vibrates 9192631770 times in an atomic clock.**1 Kelvin:**1 kelvin is the (1/273.16) part of the thermodynamics temperature of the triple point of water.**1 Candela:**1 candela is (1/60) luminous intensity of an ideal source by an area of cm’ when a source is at the melting point of platinum (1760°C).**1 Ampere:**1 ampere is the electric current which is maintained in two straight parallel conductors of infinite length and of negligible cross-section area placed one metre apart in a vacuum will produce between them a force 2 x 10-7 N per metre length.**1 Mole:**1 mole is the amount of substance of a system which contains many elementary entities (may be atoms, molecules, ions, electrons or groups of particles, as this and atoms in 0.012 kg of carbon isotope 6C

12.

### Definition of Basic and Supplementary Units

**Basic Units**

1. |
Metre (m): |
One metre is the distance travelled by light in the vacuum during a time interval of (1/299792458) seconds. |

2. |
Kilogram (kg): |
It is the mass of a platinum-iridium cylinder kept at the National Bureau of weights and measurements, Paris. |

3. |
Second (s): |
The second is the time taken by the light of a specified wavelength emitted by a caesium-133 atom to execute 9192631770 vibrations. |

4. |
Ampere (A): |
One ampere is that current which when passed through two straight parallel conductors of infinite length and of negligible cross-section kept at a distance of 1 metre apart in the vacuum produces between them a force equal to 2 x 10^{-7} newton per metre length. |

5. |
Kelvin (K): |
It is the fraction 1/273.6 of the thermodynamic temperature of the triple point of water. |

6. |
Candela (cd): |
A candela is defined as 1/60^{ th }of luminous intensity of 1 square centimetre of a perfect black body maintained at the freezing temperature of platinum (1773 ^{0}C). |

7. |
Mole (MD): |
One mole is the amount of substance that contains elementary units equal to the number of atoms in 0.012 kg of carbon-12. |

**Supplementary Units**

1. |
Radian (rad): |
The radian is the angle subtended at the centre of the circle by the arc whose length is equal to the radius of the circle. |

2. |
Steradian (Sr): |
The steradian is the solid angle subtended at the centre of a sphere by a spherical surface of an area equal to the square of its radius.2. |

### Dimensional Formula

The dimensional formula of any physical quantity is the formula that tells which of the fundamental units have been used for the measurement of that physical quantity.

**How dimensional formula is written for a physical quantity**

**(1)** The formula of the physical quantity must be written. The quantity must be on the left-hand side of the equation.

**(2)** All the quantities on the right-hand side of the formula must be written in terms of fundamental quantities like mass, length and time.

**(3)** Replace mass, length and time with M, L and T.

**(4)** Write the powers of the terms.

**Characteristics of Dimensions**

**(1)** Dimensions do not depend on the system of units.

**(2)** Quantities with similar dimensions can be added or subtracted from each other.

**(3)** Dimensions can be obtained from the units of the physical quantities and vice versa.

**(4)** Two different quantities can have the same dimension.

**(5)** When two dimensions are multiplied or divided it will form the dimension of the third quantity.

**Dimensional Analysis**

**The dimensional formula can be used to**

**(1)** To check the correctness of the equation.

**(2)** Convert the unit of the physical quantity from one system to another.

**(3)** Deduce the relation connecting the physical quantities.

### Units and Dimensions Of A Few Derived Quantities

Physical Quantity |
Unit |
Dimensional Formula |

Displacement | m | M^{0}L^{1}T^{0} |

Area | m^{2} |
M^{0}L^{2}T^{0} |

Volume | m^{3} |
M^{0}L^{3}T^{0} |

Velocity | ms^{-1} |
M^{0}L^{1}T^{-1} |

Acceleration | ms^{-2} |
M^{0}L^{1}T^{-2} |

Density | Kg m^{-3} |
M^{1}L^{-3}T^{0} |

Momentum | Kg ms^{-1} |
M^{1}L^{1}T^{-1} |

Work/Energy/Heat | Joule (or) Kg m^{2}/sec^{2} |
M^{1}L^{2}T^{-2} |

Power | Watt (W) (or) Joule/sec | M^{1}L^{2}T^{-3} |

Angular velocity | rad s^{-1} |
M^{0}L^{0}T^{-1} |

Angular acceleration | rad s^{-2} |
M^{0}L^{0}T^{-2} |

Moment of Inertia | Kg m^{2} |
M^{1}L^{2}T^{0} |

Force | Newton (or) Kg m/sec^{2} |
M^{1}L^{1}T^{-2} |

Pressure | Newton/m (or) Kg m^{-1}/sec^{2} |
M^{1}L^{-1}T^{-2} |

Impulse | Newton sec (or) Kg m/sec | M^{1}L^{1}T^{-1} |

Inertia | Kg m^{2} |
M^{1}L^{2}T^{0} |

Electric Current | Ampere (or) C/sec | QT^{-1} |

Resistance/Impedance | Ohm (or) Kg m^{2}/sec C^{2} |
ML^{2}T^{-1}Q^{-2} |

EMF/Voltage/Potential | Volt (or) Kg m^{2}/sec^{2} C |
ML^{2}T^{-2}Q^{-1} |

Permeability | henry/m (or) Kg m/C^{2} |
MLQ^{-2} |

Permittivity | Farad/m (or) sec^{2}C^{2}/Kgm^{3} |
T^{2}Q^{2}M^{-1}L^{-3} |

Frequency | Hertz (or) sec^{-1} |
T^{-1} |

Wavelength | m | L^{1} |

### Units and Measurements Notes Class 11 PDF: Solved Examples

**(1) The diameter of a cylinder is measured using vernier callipers with no zero error. It is found that the zero of the vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is**

**a)** 5.112 cm

**b)** 5. 124 cm

**c)** 5.136 cm

**d)** 5.148 cm

**Answer: b) 5. 124 cm**

**Solution:**

Least Count of a Vernier is given by

L.C = 1 Main Scale Division/Number of divisions on Vernier Scale

L.C = 1M.S.D/n

One main scale division = 0.05 cm

n = 50

L.C = 0.05/50 = 0.001 cm

Diameter of the cylinder = Main Scale Reading + (Least Count x Vernier Scale Reading)

= 5.10 + (24 x 0.001) = 5.124 cm

**(2) A thin copper wire of length l metre increases in length by 2% when heated to 10°C. What is the percentage increase in the area when a square copper sheet of length l metre is heated to 10°C?**

**a)** 4%

**b)** 8%

**c)** 16%

**d)** None of these

**Answer: a) 4%**

**Solution:**

△l = l αΔT

△l/l = 2/100 = α x 100

α = 2/1000

β = 2α = 4/1000

△A = A βΔT

△A/A = βΔT

= (4/1000) x 10

= 4/100

Percentage increase in area = (4/100) x 100

= 4%

**(3) The dimensional formula for relative refractive index is**

**a)** [M^{0}L^{1}T^{-1}]

**b)** [M^{0}L^{0}T^{0}]

**c)** [M^{0}L^{1}T^{1}]

**d)** [MLT^{-1}]

**Answer: b) [M ^{0}L^{0}T^{0}]**

**Solution:**

The relative refractive index is the ratio of the refractive index of the medium to the refractive index of the vacuum. Hence, it is a dimensionless quantity.

**You can download the Unit and Measurement Notes PDF by going through the following download link.**