Unit and Measurement

     𝕌𝕟𝕚𝕥 𝕒𝕟𝕕 𝕄𝕖𝕒𝕤𝕦𝕣𝕖𝕞𝕖𝕟𝕥𝕤

★ Units and dimensions are fundamental concepts in physics and mathematics that help describe and measure physical quantities.

★ In physics, a unit is a standard quantity used to measure a specific physical quantity. It provides a reference point against which other quantities can be compared. For example, the SI (International System of Units) unit for length is the meter (m), and the SI unit for time is the second (s).

★ Understanding units and dimensions is crucial for performing accurate calculations and ensuring consistency in scientific measurements and equations.

➞ 𝗗𝗶𝗺𝗲𝗻𝘀𝗶𝗼𝗻𝘀:- Dimensions are the powers to which the fundamental units are raised in order to express the derived unit of a quality. 

➞ 𝗣𝗵𝘆𝘀𝗶𝗰𝗮𝗹 𝗾𝘂𝗮𝗻𝘁𝗶𝘁𝘆: All quantity that can be measured are called physical quantity. 

Example:- Time, length, mass, force, etc.

➡ Classification :

(1). Based on their directional properties

➞‌ Scalar Quantity : The physical quantities which have only magnitude but no direction are called scalar quantity. 

Example : Mass, density, volume, time, etc. 

➞‌ Vector Quantity : The physical quantity which have both magnitude and direction and obey laws of vector algebra are called vector quantity. 

Example :- Displacement, force, velocity, etc.

(2). Based on their dependency

➞ Fundamental or base quantity :- A set of physical quantities which are completely independent of each other and all other physical quantities can be expressed in term of these physical quantities is called set of fundamental quantities.

‌➞ Derived Quantities :- The quantities which can be expressed in term of the fundamental quantities are known as derived quantities.

Example :- Speed, volume, acceleration, force, pressure, etc. 

➡ Classification of units

The unit of physical quantities can be classified as follows :

(1). Fundamental or base units : The unit of fundamental quantities are called base units. 

★ Note :- System of Units

1). 𝗖𝗚𝗦 = centimeter gram second . 

2).𝗠𝗞𝗦 = meter kilogram second. 

3). 𝗙𝗣𝗦 = Foot pound second . 

 ➡ SI base quantities and their units

No.  𝗣𝗵𝘆𝘀𝗶𝗰𝗮𝗹 𝗤𝘂𝗮𝗻𝘁𝗶𝘁𝗶𝗲𝘀    𝗦𝗜 𝘂𝗻𝗶𝘁𝘀    𝗦𝘆𝗺𝗯𝗼𝗹

  1                length                   meter            m

  2                 mass                   kilogram        kg

  3                 time                    second            s  

  4            temperature            kelvin            k

  5          electric current        ampere          A

  6       luminous intensity     candela         cd

  7      amount of substance     mole          mol

➡ Units of measurement

(2). Derived physical quantities

(i)  Speed = distance / time

(ii) Velocity = Displacement / time

(iii) Momentum (p) = m × v

(iv) force = m × a  etc ..examples

➞𝗗𝗲𝗿𝗶𝘃𝗲𝗱 𝗾𝘂𝗮𝗻𝘁𝗶𝘁𝗶𝗲𝘀        𝘂𝗻𝗶𝘁𝘀(𝗠.𝗞.𝗦)      𝗗𝗶𝗺𝗲𝗻𝘀𝗶𝗼𝗻

(i) Speed                                     m/s                 [ML-¹]              

(ii) Velocity                                  m/s                [ML-¹]           

(iii) Momentum                       k m/s             [MLT-¹]             

(iv) Density                                kg/m³             [ML-³]         

(v) Area                                        m²                    [L²]

(vi) Acceleration                        m/s²               [ML-²]           

(vii) Force                                 kg m / s²            [MLT-²]

(viii) Impulse                            kg m / s              [MLT-¹] 

(ix) Stress                                   kg/m s²              [MLT-²]

(x) Work                                    kg m²/s²              [ML²T-²]

(xi) Pressure                              kg/ m s²              [ML-¹T-²]

(xii) Torque or couple             kg m²/s²              [ML²T-²]

(xiii) Moment of inertia            kg m²                   [ML²]

(xiv) Power                                kg m²/s³              [ML²T-³]

(xv) gravity (g)                             m/s²                     [ML-²]  

(xvi) Potential energy                 kg m²/s²            [ML²T-²]

(xvii) Surface tension                 kg/s²                     [MT-²]

(xviii) Friction (force)                 kg m/s²               [MLT-²]

(xix) Tension                                 kg m/s²               [MLT-²]

(xx) wavelength                              m                       [ L]        

(xxi) Angular momentum          kg m²/s              [ML²T-¹]

(xxii) G = F × r²/m1 × m2              m³/kg s²          [M-¹L³T-²]

(xxiii) Coff. of viscosity                kg/m s              [ML-¹T-²]

(xxiv) Plank Constant                  kg m²/s               [ML²T-¹]

(xxv) Intensity                               kg/s³                   [MT-³]

(xxvi) Strain                                    no unit                 --

(xxvii) Angular velocity                   1/s                 [M°L°T-¹]

(xxviii) Angular acceleration          1/s²               [M°L°T-¹]

(xxix) Heat (Q)                                 kg m²/s²         [ML²T-²]         

➡️ Here are some important questions related to units and measurements along with their solutions:

1).Question: Convert 500 grams to kilograms.

Solution: Since there are 1000 grams in a kilogram, we can convert 500 grams to kilograms by dividing by 1000.

Solution: 500 grams = 500/1000 = 0.5 kilograms.

2).Question: The length of a rectangular field is 15 meters and its width is 8 meters. What is the area of the field in square meters?

Solution: The area of a rectangle is calculated by multiplying its length and width.

Solution: Area = Length x Width = 15 meters x 8 meters = 120 square meters.

3).Question: Convert 2.5 kilometers to meters.

Solution: Since there are 1000 meters in a kilometer, we can convert 2.5 kilometers to meters by multiplying by 1000.

Solution: 2.5 kilometers = 2.5 x 1000 = 2500 meters.

4). Question: The speed of a car is 60 kilometers per hour. What is its speed in meters per second?

Solution: To convert from kilometers per hour to meters per second, we need to multiply by 1000/3600.

Solution: Speed in meters per second = 60 km/h x (1000 m/1 km) x (1 h/3600 s) = 16.67 m/s (rounded to two decimal places).

5). Question: A container holds 3.5 liters of water. How many milliliters of water are in the container?

Solution: Since there are 1000 milliliters in a liter, we can convert 3.5 liters to milliliters by multiplying by 1000.

Solution: 3.5 liters = 3.5 x 1000 = 3500 milliliters.

6). Question: A student walks 500 meters in 5 minutes. What is their average speed in meters per second?

Solution: To calculate the average speed, we divide the distance traveled by the time taken.

Solution: Average speed = Distance/Time = 500 meters / 300 seconds = 1.67 meters per second (rounded to two decimal places).

7). Question: Convert 40 miles per hour to kilometers per hour.

Solution: Since there are 1.60934 kilometers in a mile, we can convert 40 miles per hour to kilometers per hour by multiplying by 1.60934.

Solution: 40 miles per hour = 40 x 1.60934 = 64.37 kilometers per hour (rounded to two decimal places).