20
Mass
By studying this lesson, you will be able to,
Ɣ identify the units used to measure mass,
Ɣ identify the relationship between the different units of mass and
Ɣ add and subtract masses given in terms of these units.
20.1 Introduction
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Now let us investigate the meaning of mass.
The mass of an object is a measure of the amount of matter in the object.
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scale which are used to measure mass.
A balance scale (weighing scale) is used to measure the mass of an
object by comparing it with the mass of one or more standard weights.
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is placed in one of the pans while the object is placed in the other pan.
Quantity of potatoes is
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Quantity of potatoes is
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The beam is
horizontal.
When the beam of the scale is
horizontal, the scale is balanced. Then
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Two 200 g standard
weights can be used to
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100 g standard weight are available,
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weight
Flour and 100 g
standard weight
20.2 Various instruments that are used to measure
mass
When a balance scale and standard weights
are used, most often, amounts which are
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weights are measured. The balance scale
and standard weights shown on page 106
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In such a situation one of the instruments shown here can be used.
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Two instruments that can be used to
measure a mass such as your body mass
are given here. When you stand on the
instrument, the indicator shows what
your mass is.
Exercise 20.1
State whether the mass of the matter in each of the following instances
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(i)
(ii)
(iii)
20.3 Relationship between different units of measuring
mass
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used to measure mass.
The relaWLRQVKLSEHWZHHQJUDPPHVDQGNLORJUDPPHVLVJLYHQEHORZ
1000 g NJ
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Activity 1
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of the following balance scales and the scale has been balanced by
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0DVVRIDZRRGHQEORFN ««0DVVRIDZRRGHQEORFN ….
7KHUHDUHZRRGHQEORFNV 0DVVRIDZRRGHQEORFN …………
Let us see whether the masses you obtained are correct.
(i) 6LQFHNJLVJWKHPDVVRIWKHZRRGHQEORFNVLV J7KHUHIRUHWKHPDVVRIRQHEORFNLVJ
(ii) 6LQFHNJLVJWKHPDVVRIWKHZRRGHQEORFNVLV J7KHUHIRUHWKHPDVVRIRQHEORFNLVJ
(iii) 6LQFHNJLVJWKHPDVVRIWKHZRRGHQEORFNVLV
J7KHUHIRUHWKHPDVVRIRQHEORFNLVJ
For free distribution
Ɣ Express a mass given in kilogrammes in terms of
grammes.
Now let us consider how we express the mass of an object which has
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6LQFH NJ 1000 g,
NJ 2000 g
NJ 3000 g
Accordingly, to express a mass given in kilogrammes, in terms of
grammes, the given number of kilogrammes needs to be multiplied
by 1000.
Example 1
Example 2
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([SUHVVNJJLQJUDPPHV
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NJ u 1000 g J
Since NJ 1000 g,
NJJ 1000 g J
J
Exercise 20.2
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(i) 7KHQXPEHURIJDPRXQWVLQNJLV«««
(ii) 7KHQXPEHURIJDPRXQWVLQNJLV«««
(iii) 7KHQXPEHURIJDPRXQWVLQNJLV«««
(iv) 7KHQXPEHURIJDPRXQWVLQNJLV«««
(v) 7KHQXPEHURIJDPRXQWVLQNJLV«««
(2) Fill in WKH EODQNV LQ HDFK RI WKH IROORZLQJ SDUWV E\ ZULWLQJ WKH
appropriate mass in grammes.
(i) 1
(ii) 1
(iii) 1
(v) 1
106
NJ
NJ
NJ
NJ
J 100 g 100 g J ...... g
JJ 100 g ...... g
4 « ...... g
(iv) 1 NJ 8 « ...... g
2 « ...... g
(vi) 1 NJ 1 « ...... g
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(3) Fill in the blanNVZLWKDVXLWDEOHYDOXH
(i)J NJ±J
(ii)J NJ±J
(4) Express the following masses in grammes.
(i)NJ (iv)NJJ
(ii)NJJ
(iii)NJJ
(v)NJJ
(vi) NJJ
Ɣ Express a mass given in grammes in terms of kilogrammes.
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J NJ
J NJ
Accordingly, to express a mass given in grammes in terms of
kilogrammes, the given number of grammes needs to be divided by
1000.
Example 1
Example 2
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and grammes.
Since 1000 J NJ
J JJ
J NJ
6LQFHJ NJ
1000
J NJJ
9 NJ
J NJJ
Accordingly, to express an amount of 1000 grammes or more, in terms
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lesser than 1000.
Example 3
Complete the following table by expressing the masses given in
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g
999
1000
6075
7009
kg
0
1
6
7
g
999
000
075
009
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Exercise 20.3
(1) Express each of the following masses given in grammes, in terms of
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(i) 2000 g
(ii)J (iii) 8000 g
(iv) 12 000 g
(2) Express each of the following masses given in grammes, in terms of
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(i)J
(ii)J (iii)J (iv)J (v)J
(3) Complete the following table by expressing the masses given in
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g
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4380
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kg
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1
3
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8
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g
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20. 4 Adding masses
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of “Thriposha”.
500 g
Both the masses have been given in grammes. Since both masses
250 g
have been given in the same unit let us add them as shown here.
750 g
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When adding these masses which have been given in terms of
NLORJUDPPHVDQGJUDPPHVLWLVQHFHVVDU\WRZULWHWKHNLORJUDPPHVLQ
one column and the grammes in a different column.
Let us add the values in the grammes column.
NJ J
JJJ J
1
500
J JJ
1
250
1
Since 1000 g NJJ NJJ
500
4
250
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Example 1
NJ
2
1
4
J
750
450
200
Let us add the amounts in the grammes column.
JJ J
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Let us write the 200 g in the grammes column.
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is,
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Exercise 20.4
(1) Write down the answers to each of the following in terms of
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(i)NJJ(ii)NJJ (iii)NJJ
2
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(iv)NJJ(v)NJJ(vi)NJJ
3
2
1
800
1
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cylinder with the gas?
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Find the total mass of these items.
A piece ofSXPSNLQRIPDVVNJJZDVFXWIURPDZKROHIUXLW
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the mass of the whole fruit.
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fruits?
20.5
Subtracting masses
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peppers that she had obtained from her
garden, out in the sun to dry for several
days. When she weighed it again she
found that the mass had reduced to 1
NJ J /HW XV ¿QG WKH TXDQWLW\ E\
which the mass had reduced during the
drying process.
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the drying process, the mass of the dried peppers has to
be subtracted from the mass of the fresh peppers. To do
1
this, let us write them one below the other, such that the 1
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values are in another column.
J
200
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Example 1
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NJ
2
0
1
J
250
750
500
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7KHQJJ J
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now. Therefore, the mass of the biscuits in the box is
NJJ
Exercise 20.5
(1) Subtract the following.
(i)NJJ
3
1
200
100
(iv)NJJ
3
1
(ii)NJJ (iii)NJJ
4
000
(v)NJJ (vi)
4
2
200
NJJ
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(2) The water in 1 kg of tea leaves was removed by drying the leaves.
The mass of the dried tea leaves was 180 g. What is the mass of the
water that was removed?
(3) The edible portion of a jackfruit of mass 3 kg was of mass 1 kg
650 g. What was the mass of the portion of the fruit that was
discarded?
(4) The quantity of sugar in Nimal’s house on Monday morning was
1 kg 500 g. On Tuesday morning, there was 800 g remaining. What
was the mass of sugar that was consumed during this period?
(5) From the 12 kg 750 g stock of lentils that was in a shop one morning,
8 kg 250 g remained at the end of the day. Find the mass of lentils
that was sold during that day.
(6) The mass of a gas cylinder with the gas is 13 kg 250 g. The mass of
the empty gas cylinder is 2 kg 450 g. Find the mass of the gas that
is in the cylinder.
(7) There was 5.85 kg of rice in a bag. If 2.17 kg of this quantity was
used for a meal, how many kilogrammes of rice was left over?
Miscellaneous Exercises
(1) Fill in the blanks.
(i)
kg
2
g
250
(ii)
kg
3
g
500
1
750
+
4
75
(2) The masses of three parcels that were brought to a post office were
respectively 2 kg 500 g, 3 kg and 1 kg 750 g. Express the total mass
of the three parcels in kilogrammes and grammes.
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(3) The masses of the items in a student’s school bag are given below.
Mass of theWH[WERRNV
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J
J
The student says that the total mass of the items in his school bag
does not exceed NJ6KRZZLWKUHDVRQVZKHWKHUWKLVVWDWHPHQWLV
true or false.
(4) The mass RIDEDJRIULFHLVNJ,IWKHPDVVRIWKHHPSW\EDJLV
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An aircraft passenger is allowed to carry a bag of personal items of
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Summary
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1000 J NJ
Ɣ To expresVDPDVVJLYHQLQNLORJUDPPHVLQWHUPVRIJUDPPHVWKH
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Ɣ To exprHVVDPDVVJLYHQLQJUDPPHVLQWHUPVRINLORJUDPPHVWKH
mass in grammes is divided by 1000.
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