MEASUREMENT  
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Measurement is the process of assigning numbers to observations or events  
Physical Quantities  
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Physical quantity is a property of a material that can be quantified by measurement.  
There are two types of physical quantities namely.  
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Fundamental quantities  
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Delivered quantities  
Fundamental Quantities  
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Are the basic physical quantities which cannot be obtained from other physical  
quantities.  
Fundamental Quantities and their SI Unit  
Quantities  
SI unit  
Unit symbol  
Length  
Metre  
m
Mass  
Kilogram kg  
Time  
Second  
S
Electric current  
Temperature  
Amount of substance  
Luminous intensity  
Ampere A  
Kelvin  
Mole  
K
mol  
Candela Cd  
Length  
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s the distance between two points.  
The SI unit of length is metre (m).  
It is measured by metre rule, tape measure, Vernier calliper and micrometer  
screw gauge  
Metre Rule  
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Metre rule is a mainly wooden graduated in 100 centimeters or 1metre.  
The reading should be perpendicular to the mark otherwise the parallax error occurs  
Parallax Error  
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s the apparent motion of one object related to another when the position of the  
eye is varied  
Vernier Caliper  
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s an instrument used to measure length to the nearest accuracy of 0.01cm  
It is used to measure lengths to the range of 1.0 cm to about 12.0 cm  
(a) The inside jaws are used to measure internal diameter  
(b) The external jaws are used to measure external diameter  
Scale of Vernier Calliper has two scales  
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Main (Fixed) scale  
Vernier scale  
NB:  
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Fixed scale gives reading in centimeter (cm) or millimeter (mm).  
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Vernier scale gives reading in hundredth of a centimeter (0.01cm) or thousands  
of millimeter (0.001mm)  
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The reading should be taken in the parallel mark between fixed scale and  
Vernier scale then convert it to cm or mm  
Total reading is obtained by Summing up the main scale (M.S) and Vernier  
scale (V.S)  
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Before using a vernier caliper, close its jaws to determine if it contains zero error  
Zero error is the error arises when scale is not starting from zero mark  
Example  
1. From the fig below, determine the diameter of the object.  
Solution:  
Give:  
Main scale, m.s = 9.9cm , Vernier scale, v.s = 2 x 0.01 = 0.02cm  
∴ 푇표푡푎푙 푟푒푎푑푖푛푔 = 9.9 + 0.02 = 9.92 푐푚  
Micrometer Screw Gauge  
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Is an instrument used to measure the length to the nearest accuracy of  
0.001cm or 0.01mm  
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It is used to measure the diameters of wires and ball bearings  
It can measure small lengths up to about 2.5 cm  
Diagram:  
Scale of Micrometer Screw Gauge:-  
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main scale (mm)  
thimble scale  
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NB:  
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Fixed scale gives reading in centimeter (cm) or millimeter (mm).  
Thimble scale gives reading in thousandth of a centimeter (0.001cm).  
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B
efore to use micrometer screw gauge close its jaws to determine if it contains  
zero error  
Example  
1. From the fig below, determine the diameter of an object.  
Solution:  
Given:  
Main scale, m.s = 9.5mm = 0.95cm ,  
Thimble scale, v.s = 31 x 0.001 = 0.031cm  
∴ 푇표푡푎푙 푟푒푎푑푖푛푔 = 0.95 + 0.031 = 0.981 푐푚  
Mass  
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Is the quantity of matter in a substance.  
The SI unit of mass is kilogram (kg).  
It is measured by beam balance.  
Other units of mass are milligram, gram, tones etc  
Their equivalence: 1t = 1000kg  
1kg = 1000g  
1g = 1000mg  
Types of Beam Balance  
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Lever arm balance (uses the principle of moments to measure the mass)  
Triple beam balance (uses the principle of moments to measure the mass)  
Digital balance (measures the mass to an accuracy of the thousandth  
(0.001g) of a gram  
Difference between Mass and Weight  
Mass  
weight  
Is the quantity of matter in an object  
Is a force of gravity on an object  
It is constant  
It varies with environment  
It is a derived quantity  
Its SI unit is Newton (N)  
It is measured by spring balance  
Is a vector quantity  
It is a fundamental quantity  
Its SI unit is kilogram (kg)  
It is measured by beam balance  
Is a scalar quantity  
Time  
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Time is the rate at which an event happens.  
It is measured by using clock or wristwatch or stopwatch  
Stopwatch  
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s a device that is held in the hand to show the time elapsed  
Types of Stopwatches  
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Mechanical stopwatch  
Digital stopwatch  
N.B: Digital stopwatch is more accurate than mechanical stopwatch. They include  
date and time  
Ways of reducing errors during measurement  
Taking several readings and then find the average  
Avoiding parallax error by positioning te instrument properly on the table with  
eyes perpendicular to the scale  
Some instruments cab be adjusted to eliminate zero error  
Delivered Quantities  
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Are the physical quantities which are expressed in terms of the fundamental  
quantities  
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Examples are area, volume, weight, pressure etc  
Volume  
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s the quantity of space that an object occupies.  
Its SI unit is cubic meter (m3)  
N.B  
1L = 1000 cm3  
1L = 1000 ml  
1L = 1dm3  
Volume of a solid regular object  
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R
egular object is the object with known shape.  
For example, cylinder, rectangular prism, cube etc.  
The Volume of an object is given by:-  
V = A x h  
Whereby  
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A = area of a regular object  
h = height of a regular object  
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Volume of a Cube  
Volume of a cube , V = w x b x h = 풘 × 풘 × 풘  
Since w = h = b  
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Volume of Rectangular prism  
Volume of rectangular prism ,V = w x b x h  
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Volume of Cylinder  
Volume of cylinder =  
흅
r2 h  
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Volume of Sphere (h = r)  
ퟒ흅푹ퟑ  
ퟑ
푽풐풍풖풎풆 풐풇 풔풑풉풆풓풆 (푽) =  
Example  
1. Calculate the volume of rectangular block of sides 15cm, 8cm and 7cm  
Solution:  
V = 15 cm x 8 cm x 7 cm = 840 cm3  
Individual Task – 1  
1. Calculate the volume of cylinder whose radius and height are 5 cm and 14 cm  
respectively. Given that π = 3.14.  
(ANS: V = 1099 cm3)  
Volume of Liquid  
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Litre is the standard unit used for measuring the volume of liquids.  
Burette, Pipette, measuring cylinder are examples of the instruments or  
apparatus used to measure the volume of liquids  
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During measurement the eye should be in the same line with the meniscus of  
the liquid  
Volume of Gas  
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The volume of gas is obtained by measuring the volume of the container into  
which it is put  
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And the volume of the container can be determined from its dimensions or by  
filling it with water and then pouring the water into a graduated cylinder  
Thus VGAS = V(CONTAINER + GAS) – V(CONTAINER)  
Volume of an irregular object  
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Irregular object is the object with unknown shape.  
For example, stone, human body etc.  
The volume of irregular object is obtained by displacement method or  
immersion method  
Displacement Method  
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Volume of irregular object is based on the principle that when an object is completely  
submerged in water it displaces a volume of water equal to its own volume.  
The volume of irregular object can be measured by using:  
(a) A Graduated cylinder  
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(b) A Eureka can or overflow can  
Graduated Cylinder  
Suppose you want to measure the volume of a small stone. The following  
steps are necessary: -  
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Fill a graduated cylinder to known mark (let it be 300ml)  
Carefully measure the initial volume of water (V1)  
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Gently lower the stone into the water  
Measure the final volume of water (V2)  
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Lastly find the difference between the final and initial volume of water. This  
gives the volume of a stone. That is VSTONE = V2 – V1  
Example  
1. When an irregular solid was immersed in 65cm3 of water the water level rises  
to 81cm3. What was the volume of the solid?  
Solution:  
Volume of the solid, V = V2 – V1 = 81 – 65 = 16 cm3  
Using Eureka Can (Over flow can)  
Consider the following steps: -  
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Fill the overflow can with water up to the level of the spout  
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Tie the irregular solid (stone) with a string  
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Gently drop the irregular solid into water using a string  
The irregular solid (stone) will displace some water which will be collected in  
the beaker  
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Transfer the displaced water into a graduated cylinder  
Measure the volume of water, which is the volume of irregular solid  
Importance of Measurement  
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It is used in architecture and engineering for designing of bridges, flyovers and  
other structures  
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It is used in school to determine the number of students  
Measurement for length are used for fitting clothes in the fashion industry  
In trade – exact quantities for export or import are to be known  
Helps to identify the space occupied by substance  
Helps us to know the rate of working  
Helps us to identify the size of substance  
It helps in decision making