Units and Measurements PDF Study Notes

Units and Measurements PHYSICS Copyright © 2014-2020 TestBook Edu Solutions Pvt. Ltd.: All rights reserved  Download Testbook App Units and Measurements Definition Physical Quantity : The quantities which can be measur...

Units and Measurements PHYSICS Copyright © 2014-2020 TestBook Edu Solutions Pvt. Ltd.: All rights reserved  Download Testbook App Units and Measurements Definition Physical Quantity : The quantities which can be measured or defi ned are known as physical quantities. Some examples are force, distance, time, etc. The process of comparison of an unknown quantity with a standard quantity is known as "Measurement". Two parameters are used to express the result of measurement of a physical quantity. They are as follows: 1) Magnitude: By this parameter, it is expressed that how many times the above selected unit is contained in the given quantity. 2) Unit: For understanding any physical quantity, its classifi cation or comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard is called unit. For example, in a force of 20 Newton, ‘force’ is the physical quantity, ‘20’ is the magnitude, and ‘newton’ is the unit of force. The result of the measurement of any physical quantities is expressed by number (its numerical measurement) accompanied by a specific unit. In physics, we have many such physical quantities and hence a variety of units but for better understanding and classification, we need only a few limited numbers of units that can relate with one another. Definition Fundamental Units: The units for the fundamental or basic quantities are known as fundamental or base units. There are 7 base or fundamental unit (length, mass, time, electric current, temperature, amount of substance, luminous intensity) PHYSICS | Units and Measurements PAGE 2  Download Testbook App Units As explained earlier, measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit. A complete set of these units, both the base units and derived units, is known as the system of units. There are three such systems which are generally used. The base units for length, mass and time in these systems are as follows: 1) In the CGS system they were centimeter, gram and second respectively. 2) In the FPS system they were foot, pound and second respectively. 3) In the MKS system they were a meter, kilogram and second respectively. Q. The surface tension of a liquid is 90 dyne/cm. In MKS system its value is? A. The surface tension of a liquid is 90 dyne/cm. In MKS system or SI unit its value is 9 x 10-2 N/m.  1 dyne/cm = 1 x 10-3 N/m  A British Association for the Advancement of Science first suggested the name dyne as a centimeter–gram–second (CGS) force unit in 1873.  It is a derived force unit defined in the unit's framework of centimeter–gram– second (CGS).  Newton is a unit of force derived from the International System of Units (SI), whereas the MKS (Meter, kilogram and sec) is used to define SI Units.  In honor of his research on classical mechanics, it is named after Isaac Newton, specifically the second law of motion of Newton. MKS system has been adopted as an international system and called S.I. units. The reason for adopting this system is due to the ease of conversion from large quantity to small or vice-versa just by multiplying it by powers of 10, known as a prefix. E.g.- 1 meter can be converted into centimeter by multiplying it by 102. i.e., 2 m ⇒ 2×102 = 200 cm and vice versa. PHYSICS | Units and Measurements PAGE 3  Download Testbook App Standard Prefixes Sometimes when the numerical value of a quantity becomes very large or very small, prefixes are used along with the units to make the numerical values of the quantities more manageable. Factor Prefix Symbol For small measurements 10-1 Deci D 10-2 centi C -3 10 Milli m 10-6 Micro µ 10-9 Nano n 10-12 Pico p 10-15 femto f 10-18 atto a 10-21 zepto z 10-24 yoeto y For large measurement 1024 Yotta Y 1021 Zetta Z 1018 exa E 1015 Peta P 12 10 Tera T 109 Giga G 106 Mega M 103 Kilo K 102 hecto H 101 Deca da PHYSICS | Units and Measurements PAGE 4  Download Testbook App Memory Tip Deci Q. If we have 15 kg of rice what will be the equivalent amount in grams A. For 15 kg equivalent amount will be 15 kg ⇒ 15 × 103 g Hence for 15 kg of rice the equivalent amount will be 15,000 g of rice. Note: In this example we are also converting SI unit to CGS unit since the SI unit of mass is the kilogram (kg) and CGS unit is grams (g) Types of Quantities All physical quantities are generally classified into two types: 1) Fundamental quantities 2) Derived quantities PHYSICS | Units and Measurements PAGE 5  Download Testbook App Fundamental Quantities Fundamental quantities are those quantities that cannot be derived from any other quantities. In the SI Unit, there are 7 fundamental quantities, Besides the seven base units, there are two more units called supplementary units that are defined for a) plane angle dθ as the ratio of the length of arc ds to the radius r and b) solid angle dΩ as the ratio of the intercepted area dA of the spherical surface Fundamental units: The units for the fundamental or base quantities are called fundamental or base units. Some examples and their respective SI and CGS units are as follows. Base quantity Dimension Symbol (S. I unit) Symbol (CGS system) Length [L] M (metre) cm (centimeter) Mass [M] Kg (Kilogram) g (gram) Time [T] s (Second) s (Second) Electric Current [A] A (Ampere) A (Ampere) Temperature [K] K (Kelvin) °C (Degree Celsius) Amount of substance [mol] mol (Mole) - Luminous intensity [J] cd (Candela) - Supplementary quantities Angle - Radian (rad) - Solid angle - Steradian (sr) - PHYSICS | Units and Measurements PAGE 6  Download Testbook App Derived Quantities The quantities which can be derived from fundamental quantities or which consist of fundamental quantities are called derived quantities. Derived units: The units of all other physical quantities can be expressed as combinations of the base units. Such units obtained for the derived quantities are called derived units. Q. What will be the S.I unit of kinetic energy in terms of its respective fundamental quantity? A. Kinetic energy is the energy carried by the particle by the virtue of its motion and it is expressed as : ∴ Unit of K.E = kg m2/s2 Here we can ignore the constant ½ since its unit-less and we are only concerned with the unit of kinetic energy. Note: From this, we can say that unit of kinetic energy must be kg m2/s2 but also the SI unit for kinetic energy is Joule ∴ 1 joule = 1 kg m2/s2 Physical Quantity Symbol Dimension Measurement Unit Area A L2 square meter m2 Volume V L3 cubic meter m3 Velocity v L/T meter per second m/sec Angular velocity ω T-1 radians per second 1/sec Meter per square Acceleration a LT-2 m/sec2 second radians per square Angular acceleration α T-2 1/sec2 second PHYSICS | Units and Measurements PAGE 7  Download Testbook App Force F MLT-2 Newton Kg m/sec2 Energy E ML2T-2 Joule Kg m2/sec2 Work W ML2T-2 Joule Kg m2/sec2 Heat Q ML2T-2 Joule Kg m2/sec2 Torque τ ML2T-2 Newton meter Kg m2/sec2 Power P ML2T-3 watt & joule/sec Kg m2/sec3 kilogram per cubic Density D or ρ ML-3 Kg/m3 meter Newton per square Pressure P ML-1T-2 Kg m-1/sec2 meter Impulse J MLT-1 Newton second kg m/sec Kilogram square Inertia I ML2 kg m2 meter lumen Luminous flux f C (4Pi candle for a point cd sr source) lumen per square Illumination E CL-2 Cd sr/m2 meter Entropy S ML2T-2K-1 joule per degree kg m2/sec2 K cubic meter per The volume rate of flow Q L3T-1 m3/sec second Kinematic viscosity n L2T-1 square meter m2/sec Newton second per Dynamic viscosity m ML-1T-1 kg/m sec square meter Measurement of Length Range of Lengths may vary from the26size of the order of 10 –14 m of the tiny nucleus of an atom to the size of the order of 10 m. Some Important conversions are:  Nautical Mile: Used to measure distance in the seas and oceans. 1 nautical mile = 1852 m  Fathom: Used for measuring the depth of the ocean. 1 Fathom = 1.828 m = 6 feet PHYSICS | Units and Measurements PAGE 8  Download Testbook App  Light year: The distance traveled by light in a vacuum in one year. 1 light-year = 9.46 × 1015 m  Parsec: It is the largest unit of distance and known as Parallactic Second. 1 parsec = 3.26 light year  Astronomical Unit (AU): The mean distance between the sun and the earth. 1 AU = 1.496 × 1011 m Measurement of length using Parallax theorem Large distances such as the distance of a planet or a star from the earth cannot be measured directly with a meter scale. So, we use the parallax method for this type of measurements. When you hold a pencil in front of you against some specific point on the background (a wall) and look at the pencil first through your left eye A (closing the right eye) and then look at the pencil through your right eye B (closing the left eye), you would notice that the position of the pencil seems to change with respect to the point on the wall. This is called parallax. The distance between the two points of observation is called the basis. To measure the distance D of a faraway planet S by the parallax method, we observe it from two different positions (observatories) A and B on the Earth. As the planet is very far away, b