Measurement
We perform various activities in our daily life. While performing such activities, we need to take the measurement of several things. Measurement of an object is to find the accurate quantity of the object. In ancient time, people used to apply various traditional methods for measurement. The length was used to be measured by cubit palm, angul, bitta, mana, pathi etc. These ways of measurement had no uniformity because the size of a hand varied from person to person. That's why people used certain measurement as standard measurement unit. In Nepal, units such as mile, gauge, foot were used to measure length and paau, sher, dharni were used to measure the mass whereas maana, pathi, murri were used to measure the quantity of grains. There was no uniformity of such measurement systems with other countries. So, it was necessary to bring change for the uniformity in the measurement. In order to fulfill this lacking, an internationally recognized unit i.e. SI unit was accepted all over the world.
SI Unit
The international convention of scientists held in Paris in 1960 decided to adopt an international system of unit which is known as SI unit (System International de units). According to this system, the various fundamental units are as follows:
Physical Quantity and their fundamental units.
Length Metre (m) Mass Kilogram (kg)
Time Second (s) Temperature Kelvin (K)
Electric Current Ampere (A) Luminous Intensity Candela (cd)
Amount of Substance Mole (mol)
Those above mentioned units of measurement are accepted universally. 1 metre should have exactly the same length in every part of the world or elsewhere. Similarly, 1 kilogram mass refers the same quantity of an object all over the world.
Now carry out the given exercise
Length
The distance between two points is called length. Height of the person means the distance between the top of head to his feet. The length, breadth, height, thickness, depth, diameter,etc are examples of the length.
Measurement of length
Activity 1
List out the measuring scales used in your surrounding and write their uses The uses of scale depends upon their structure. Shorter length is measured by using small scale whereas longer length is measured by using measuring tape. The measuring tape is portable and can be rolled up after its use. The small and hard scale of geometry box helps to draw straight lines. It is easier to measure the length of the clothes with hard iron scales in cloth shopes.
Unit of length
The SI unit of length is metre(m). There are so many smaller and longer units besides metre. The relationship among them is given below.
10 millimetre (mm) = 1 centimeter (cm) 10 centimetre (cm) = 1 decimetre (dm)
10 decimetre (dm) = 1 metre (m) 10 metre (m) = 1 decametre (dam)
10 decametre (dam) = 1 hectometre (hm) 10 hectometre (hm) = 1 kilometre (km)
Out of these units of length, millimetre, centimetre, metre and kilometre are in common use.
1 centimeter (cm) = 10 millimeter (mm) 1 metre (m) = 100 centimeter (cm)
1 kilometer (km) = 1000 metre(m)
Ways of Measuring length accurately
You should take the following precautions in order to measure the length of an object correctly:
1. Error due to wrong sight angle
The measuring scale used may be thick. While measuring with thick scale the reading becomes either more or less than the actual value. In figure, the reading by the eye of position 'a' & 'c' gives the incorrect reading whereas reading by the eye of position 'b' gives the correct reading. The eye should be placed exactly above the point from which the length is to be measured.
2. Error due to damaged edges of measuring scale
After using the scale for a long time, its end begins to corrode. Do not use the ends of a corroded scale while taking measurements. The edges of scale some times get damaged with use and this can lead to errors. We must not start from the damage edge. Instead we should start from some other mark to get correct measurement.
Wrong measurement Correct measurement
3. Error on the position of scale
The ruler (scale) should be placed parallel to the measuring side. There will be error if the scale is placed on slanting to the measuring side.
Wrong measurement Correct measurement
Measurement of diameter of a spherical body
Place the spherical body in between two rectangular blocks in a plane surface. Place a scale between the faces of two blocks and measure their distance. This gives the diameter of the sphere.
Activity - 2
Measure the length, breadth, height or thickness, circumference and external diameter of Geometry box, Science book, Coin, Bench, Blackboard
The length, breadth, height, thickness, circumference, diameter, etc. can be measured by using scale.
Mass
The amount of the matter contained in a body is called its mass. A light object contains less matter in it. So, it has less mass. Similarly, a heavy object contains more matter in it. So, it has more mass.
Measurement of mass
In order to find out the mass of an object, we need to measure the object by using a physical balance. A physical balance has two pans. The body whose mass is to be measured is kept in one pan and standard weights are kept in other pan. The beam of physical balance becomes horizontal when the mass of the objects is equal to the total mass of the standard weights on the other pan. The pointer at the centre of physical balance is given to check whether the masses in two pans are equal or not. The pointer at the centre becomes vertical when the mass of unknown object kept in one pan is equal to the total of the standard weights kept in another pan.
Unit of mass
The SI unit of mass is kilogram (kg). There are other units of mass which are smaller or bigger than kilogram.
1 ton = 1000 kilograms (kg) 1 kilogram (kg) = 1000 grams (g)
1 gram (g) = 1000 milligrams (mg)
Activity - 3
Take a physical balance and its standard weights. Put the objects whose mass is to be determined at the left pan of the balance. In the other pan, keep on adding standard weights one by one till the beam of the balance becomes horizontal. If the beam of the balance is horizontal, note the mass of the standard weights.
Thus, noted mass of the standard weights is equal to the mass of the objects of left pan.
Time
The interval between two events is called time. Such as the rising of the sun from the east is an event. The rising of the sun on the next day is another event. The interval between these two events is the time of one day. Similarly a day is divided into 24 equal interval. Here day, (second, minute, hour) night, month, year, etc. are the units of time.
Measurement of time and its unit
Time is measured by using clocks or watches. There are different kinds of clocks and watches. The fundamental SI unit of time is second.
Therefore, 1 solar day = 1 ×24 hours
= 24×60 minutes = 1440 minutes
= 24 × 60 × 60 second
= 86400 seconds
1 day has 86400 seconds.
1 second is defined as (1/86400) part of one solar day.
That is 1 second = (1/86400) day
Different types of watches are used to measure the time. For example: simple watch, digital watch, atomic watch, etc.
In our simple watch, few seconds may fluctuate from the exact time. So, scientists use atomic watch to measure the accurate time.
Area
The plane surface covered by a body is called its area. It is measured in square metre or square centimeter.
Regular and irregular objects
Activity - 4
Place a coin in a paper and draw its outer surface with the help of a pencil. Put the coin up and observe how much space does it occupy. The plane space occupied by that coin on the paper is its area. In the same way, the space occupied by our foot in the ground is the area of our foot.
Activity - 5
Take a piece of a stone, a brick and a book. Now observe their outer surfaces. What differences do you see in their shapes? How is the surface of the book or brick? Is their surface regular or not? Is the surface of the stone regular? Compare it. Several objects around us which have geometrical shapes are called regular objects. They have fixed shape such as, bricks, books, copy, marbles, ball, etc. The objects which don't have fixed geometrical shapes are called irregular objects. Such as, piece of stones, pieces of bricks, pieces of paper ,etc.
Area of regular plane surface
Several objects around us have various shapes. Among them, some have fixed and regular shape. Such as coin is circular in shape. Books and copies are rectangular in shape. By using various formula, we can calculate the surface area of such regular objects. The formula to calculate the area of some regular shaped objects are as follows:
a. Area of rectangle (A) = length (l) x breadth(b)
b. Area of square object (A) = (length)2 = l2
c. Area of circular object (A) = πr2 (π = 22/7) (r = radius)
Example 1
If a rectangular room is 5 metre long and 3 metre wide, then find the area of the room?
Solution:
Here,
Length of the room (l) = 5m
Breadth of the room(b) = 3m
Area of the room (A) = ?
According to formula
Area (A) = l x b
= 5 m × 3 m = 15 m2
∴ The area of the room is 15m2.
Activity 6
Find the area of the cover page of your Science and Environment book by using formula. Similarly, find out the area of your classroom by measuring its length and breadth.
Area of irregular plane surface
Several objects around us do not have fixed shape. For example, a piece of paper, a piece of stone, a leaf, etc. They have irregular shape. We can't determine the area of such objects by using formula. We can determine the area of an irregular surface by using a graph paper.
Activity 7
Take a graph paper and place it on the table. Put a piece of stone over the graph paper and trace the boundary of the stone. Remove the stone and count the number of enclosed squares. While counting the squares, the number of full and more than half enclosed square should be counted, while less than half are ignored. The number of square thus counted gives the area of that stone.
Volume
In our daily life we need different liquids like milk, kerosene, petrol, diesel, etc. How can we measure their volumes? Do you know? Have you ever been to shop to buy kerosene? Which instrument does the shopkeeper use to measure those liquids?
In ancient time, those liquids were measured in Maana and pathi but liter was not used on those days,why?
Litre is unit of volume of liquid. When liquid is kept in a measuring vessel, it occupies space. The space occupied by liquid is its volume. The space occupied by any object is called its volume. It is measured in cubic metre (m3). The volume of liquid is also measured in litres. 1 cubic metre is equal to 1000 litres.
Measurement of volume of liquid
Activity 8
Take a measuring cylinder and pour some amount of water in it. What is the shape of the surface of water in measuring cylinder? Observe carefully. Is the level of water plane? The level of water is not a plane but curved such that the middle portion more depressed than its sides. Such a curved surface is called concave surface. Water, oil, kerosene, alcohol, spirit, etc. wet glass surface. So, they form a concave surface in a glass vessel. Though mercury is a liquid, it doesn't stick on the glass surface. The mercury liquid surface is more depressed at the sides than at the middle. Such type of surface is called convex surface.
The volumes of the liquids which make concave shape is measured from the lower meniscus. Whereas the volume of the liquids which make convex shape is measured from the upper meniscus. While taking the reading of water level, the eye should be kept straight at the same level of liquid. If the eye is kept lower than the water level, the volume of water seems less lower than its actual value and if the eye is kept above the water level, the volume of water seems more.
Volume of regular solid objects
Have you ever seen the box of chalk, matchsticks, bricks? What are their shapes? Those objects are rectangular in shape. Volume of such objects can be determined easily. Volume of such rectangular objects can be determined by measuring its length, breadth and height or width.
Volume of rectangular object = length (l) x breadth (b) x height (h)
\ V = l x b x h
In a cube, its all sides are equal. So, the volume of a cube is given by formula.
Volume of cube (V) l x l x l = l3 or (side)3
Volume of Sphere
The objects like marble or ball is sphere.
Volume of sphere = 4/3pr3 x (radius)3
V = pr3 where p = 22/7
Volume of irregular solid objects
Take a measuring cylinder and fill it partially with water. Mark the level of the water and note down. Take a stone and tie it tightly with a string and lower it slowly into the cylinder. The water level rises. Note down the water level. Now, find the difference between the two of water levels, which gives the volume of the stone.
Suppose : Initial water level = V1
Water level with stone = V2
The water level rises. Note down the water level. Now, find the difference
between the two of water levels, which gives the volume of the stone.
Suppose : Initial water level = V1
Water level with stone = V2
Then, volume of stone (V) = V2 - V1
Example : 2
In the adjoining figure, calculate the volume of the stone immersed in water.
Solution
Here, Initial volume of water (V1) = 200 cm3
Volume of water along with stone (V2) = 250cm3
Volume of stone (V) = ?
Now, V = V2 - V1
= 250cm3 - 200cm3
= 50 cm3
Therefore, volume of the stone is 50cm3.
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