JAMNABAI NARSEE SCHOOL ESTIMATION AND UNITS. Std 8

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1 JAMNABAI NARSEE SCHOOL ESTIMATION AND UNITS Std 8 Order of magnitude Definition: The order of magnitude of a physical quantity is its magnitude in powers of ten when that physical quantity is expressed in powers of ten with one digit to the left of the decimal. Note: The measure of a physical quantity can be expressed as : M x 10 n. If M < 3.2, the order of magnitude remains 10 n. But if M > 3.2 then the order of magnitude will become 10 n+1. The following examples will clear the concept: Some examples of order of magnitude: 1) Mass of an electron = 9.1x10-31 kg Here, since M = 9.1, which is > 3.2, so the order of magnitude changes to 10 n+1, i.e order of magnitude changes to = ) Charge on an electron = 1.6x10-19 coulomb. Here, since M = 1.6, which is < 3.2, so the order of magnitude stays as 10 n, i.e.order of magnitude = ) Diameter of hydrogen atom = 1.02 x10-10 m Here, since M = 1.02, which is < 3.2, so the order of magnitude stays as ) Radius of earth = 6.378x10 6 m Here the order of magnitude will be = ) Mass of earth = 5.983x10 24 kg Here the order of magnitude will be = ) Speed of light = 3x10 8 m/s Here the order of magnitude will stay as 10 8.

2 Unit :Units are of two kinds: 1) Fundamental or Basic Units 2) Derived Units Definition: Fundamental Units: A fundamental unit is that which is independent of any other unit or which can neither be changed nor can it be related to any other fundamental unit. Examples: The units of length, mass, time, temperature, current and amount of substance are independent of each other. Definition: Derived Units: Derived units are those which depend on fundamental units or which can be expressed in terms of fundamental units. Examples: Area, volume, speed etc. In mechanics, length, mass and time are the three fundamental quantities. They are independent of each other and all quantities can be related with them. Four main systems of measurement are given below: System Name Unit of Length Unit of Mass Unit of Time Unit of Current C.G.S System centimeter(cm) gramme(g) second(s) - F.P.S System foot(ft) pound (lb) second(s) - M.K.S System metre(m) kilogramme(kg) second(s) - M.K.S.A System metre(m) kilogramme(kg) second(s) ampere(a) Note: Now we use the S.I System of Units which is an enlarged and modified version of the metric system. Systeme Internationale d Unites (or S.I System) For S.I System, the following table gives the fundamental quantities, their units and their standard symbols. Sr.No Quantity Unit Symbol 1 Length metre m 2 Mass kilogram kg 3 Time second s 4 Temperature kelvin K 5 Luminous intensity candela cd 6 Electric current ampere A 7 Amount of substance mole mol 8 Angle radian rd 9 Solid angle steradian st-rd For expressing large measurements, we use deca, hector, kilo as prefixes with the units. The symbol and meaning of each prefix are given below: Sr. No. Prefix Symbol Meaning

3 1 deca da hector h kilo k mega M giga G tera T The various small measurements are expressed by using the prefixes deci, centi, milli, micro etc with the units. The symbol and meaning of each such prefix is given below: Sr. No. Prefix Symbol Meaning 1 deci d centi c milli m micro µ nano n pico p Units of length: In the S.I System, the length is measured in unit meter (m). Sub-units of meter: centimeter(cm), millimeter(mm), micron (µ) and nanometer (n). Note: 1cm = 10-2 m 1mm = 10-3 m Micron: It is one millionth (10-6 ) part of a meter. It is expressed by the symbol µ. It is also called micrometer. 1 micron (µ) = 10-6 m. Multiple units of meter:kilometer(km) 1km = 10 3 m. Non-metric units of length: Bigger units: For the measurement of the distance between heavenly bodies, the kilometer is considered too small a unit. The commonly used unit for this purpose is the astronomical unit (A.U.), light year (ly), and parsec. Definition: Astronomical Unit (A.U) - one astronomical unit is equal to the mean distance between the earth and the sun. Light year (ly) A light year is the distance travelled by light in vacuum in one year, i.e. 1 light year = speed of light in vacuum x time (1year) Parsec one parsec is 3.26 times the light year. Smaller Units: To express the size of a molecule and atom, a small size unit called the angstrom (Ǻ) is used, while the size of the nucleus is expressed in a still smaller unit fermi (f). Angstrom (Ǻ): It is 10-10th part of a meter.

4 Fermi (f): It is 10-15th part of a meter. Units of mass: In S.I system, mass is measured in kilogramme(kg). Sub units of kilogramme are gramme(g) and miligramme(mg). 1kg = 100g, 1mg = 10-6 kg or 10-3 g Multiple units of kilogramme: 1 quintal = 100kg, 1 metric tonne = 100kg = 10quintal Non-metric units of mass: The mass of atomic particles such as proton, neutron, electron is expressed in a unit called the atomic mass unit (a.m.u) Definition: 1 a.m.u is th the mass of one carbon-12 atom. Units of time: The S.I unit of time is second(s). Other common units of time are minute, hour, day, month, lunar month, year, leap year, decade, century and millennium. Note: 1) Lunar Month: It is the time in which the moon completes one revolution around the earth 2) Decade: A decade consists of ten years. 3) Century: A century consists of hundred years. 4) Millennium: A millennium consists of 1000 years. Some examples of Derived Units: Sr.No Quantity Definition Derived Unit Symbol 1 Area length x breadth metre x metre m 2 2 Volume length x breadth x metre x metre x metre m 3 height 3 Density kilogram/(metre) 3 kg m -3 or kg/m Speed or Velocity m s -1 or m/s Acceleration m s -2 or m/s 2 6 Force mass x acceleration kilogram x metre second 2 OR newton kg m s 2 OR kg.ms -2 OR N 7 Work and Energy Force x displacement kilogram x metre x metre (second ) 2 Or joule kg m 2 s -2 OR J 8 Momentum Mass x velocity kilogram x kg m s -1

5 9 Moment of a force or torque Force x distance kilogram x metre x metre (second ) 2 kg m 2 s Power Work kilogramme (metre) 2 second kg m 2 s -3 Time (second) 2 OR joule/second or watt OR J s -1 OR W 11 Pressure Force Area kilogramme x metre (metre) 2 ( second ) 2 kg m -1 s -2 OR Pa OR pascal 12 Frequency or second -1 or hertz s -1 or Hz Guidelines for writing the units: 1) If a symbol is not named after a scientist, it is written in lower case, for example metre is (m), second is (s). 2) If the symbol for a unit is named after a scientist, its first letter is capital. For example N for newton, J for joule, W for watt, Pa for pascal, Hz for hertz, C for coulomb and V for volt. 3) The full name of the unit, even when it is named after a scientist, is written with lower initial letter eg. unit of force is written as newton and not Newton. Unit of energy is written as joule and not Joule. 4) A compound unit formed by multiplication of two or more units is written after putting a dot, cross or leaving a space between the two symbols eg. Unit of torque is written as N.m or N m 5) Negative power is used for compound units, which are formed by dividing one unit by the other eg. The unit for velocity is which is expressed as m s -1. 6) A unit in its short-form is never written in plural. For example 10 metres cannot be written as 10ms because ms would imply metre x second.so it is simply written as 10m.

6 QUESTION BANK 1. Define a fundamental quantity. 2. Name the three fundamental quantities. 3. What are the fundamental units of the S.I System? Name them along with their symbols. 4. Explain the meaning of derived units along with the help of one example. 5. Which of the following is NOT a fundamental unit? a) metre b) litre c) kilogramme d) second. 6. Name two units of length which are bigger than a metre. How are they related to metre? 7. Name the three convenient units used to measure length ranging from very short to very long. 8. Which of the following is NOT a unit of distance? a) light year b) parsec c) leap year d)angstrom 9. Name the S.I. unit of mass. 10. Give two points of difference between fundamental and derived units 11. Define 1 a.m.u 12. Complete the following : a) 1g = kg b) 1mg = kg c) 1quintal = kg d) 1 metric tonne = kg 13. What is a leap year? 14. What is a lunar month? 15. Write the derived units of the following a) speed b) acceleration c) force d) density e) area 16. Complete the table: Sr. No. Quantity Unit Symbol 1 cd 2 mole 3 mass 4 K 5 A 6 time 17. The size of a bacteria is 1µ. Find the number of bacteria in 1m length.

7 18. Define: a) Astronomical unit b) Light year c) Parsec d) Angstrom e) Fermi 19. Fill in the blanks: a) 1 decade = years b) 100 years = century c) A millenium = years 20.Correct the following: a) Unit of force is Newton (n). b) Symbol for metre is (M) c) Unit of power is Watt (w). d) Length of a string, 10 metres long, can be written as 10ms.