NCERT Solutions Class 6 Science Chapter 5 Measurement of Length and Motion

F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T

CLASS 6 · SCIENCE

NCERT Solutions

Chapter 5: Measurement of
Length and Motion

NCERT Textbook — Curiosity

BOOK PAGES SECTIONS QUESTIONS MEDIUM

79 – 100 17 48 English

Solutions, notes, sample papers & more at 65 pages

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

CLASS 6 · SCIENCE · CURIOSITY

NCERT Solutions — Chapter 5: Measurement of Length
and Motion
Complete NCERT Solutions for Class 6 Science Chapter 5 Measurement of Length and Motion from the
NCERT textbook Curiosity. Every question is answered — all seven Activities (5.1 to 5.7), the in-text and Think
it over! questions from pages 79 to 95, and all 13 questions of Let us enhance our learning plus the six
Learning further projects — with each unit conversion worked out step by step.

TEXTBOOK BOOK PAGES

Curiosity (Class 6) 79 – 100

SECTIONS QUESTIONS

17 48

MEDIUM

English

In-text Questions — Page 79
Chapter opener — Deepa gets a new uniform

Q1 Are the tape and rod similar to the scale that the elder sister has in her geometry
box? What did mother mean by char angula?

Yes — all three are measuring instruments for length, but each is built for a different job.
And char angula means “four finger-widths”, roughly 6 cm to 8 cm of extra cloth.

INSTRUMENT WHAT IT IS LIKE BEST USED FOR

Metal measuring rod A stiff, straight rod, usually one Cloth spread flat on a counter —
(shopkeeper) metre long straight lengths

Measuring tape (tailor) A long, soft, flexible strip that can Chest, waist, sleeve — lengths along a
bend curved body

15-cm scale (geometry box) A short, stiff plastic ruler marked in A pencil, an eraser, lines in a notebook
cm and mm

So they are similar in purpose — every one of them carries markings and tells you a length in
the same units — but they differ in length and in stiffness.
What is char angula?

Page 1 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

angula = the width of one finger

char angula = 4 × width of one finger

1 finger width ≈ 1.5 cm to 2 cm
So char angula ≈ 4 × 1.5 cm to 4 × 2 cm = 6 cm to 8 cm

Deepa's mother wanted the uniform to be about 6–8 cm longer, so that it would still fit after
Deepa grows a little more.

Why it happens: angula is one of India's ancient units of length, mentioned along
with dhanusa and yojana in old texts and still used by carpenters and tailors. It is a
body-based unit, so it is quick and handy — you always carry your fingers with you
— but it is not the same for everybody. The tailor's four fingers may not equal your
mother's four fingers.

Try This: Measure the width of your own index finger with a 15-cm scale, and then
your father's or mother's. Write both in mm. The difference you find is exactly the
reason the world needed standard units.

In-text Questions — Page 81

Page 2 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

5.1 How do we Measure?

Q1 Oh, the number of handspans is different for all of us. So, what can we say about
the length of the table?

NAME OF THE STUDENT NUMBER OF HANDSPANS

Anish Slightly more than 13

Padma 13

Tasneem Slightly less than 13

Deepa Between 13 and 14

Hardeep 14

Table 5.1, page 81 — the length of the same table, measured by five children in their own
handspans.

Very little that is useful! All we can honestly say is that the table is about 13 to 14 handspans
long — and even that sentence is incomplete, because it does not say whose handspan.

NAME OF THE STUDENT NUMBER OF HANDSPANS

Anish Slightly more than 13

Padma 13

Tasneem Slightly less than 13

Deepa Between 13 and 14

Hardeep 14

The length of the table never changed while the five friends measured it. Only the unit changed
— and so the number changed.

Page 3 of 65

as e
a
Class 6 Science Chapter 5 Measurement of Length and Motion
g l AglaSem · NCERT Solutions

co m
em.
Length of table = number × size of one handspan
m l as
.co
The length is fixed, so a bigger handspan gives a smaller number,
m a g
l a se
g
and a smaller handspan gives a bigger number.
a

co m
A measurement is only meaningful if the person hearing it can reproduce it. “13 handspans”

m .
cannot be reproduced by anyone else, so it is not a proper measurement of the table. We
e ag
need a unit that is the same for everybody.
g l as
a
Why it happens: a length is expressed in two parts — a number and a unit. If the

co m
m.
unit is not fixed, the number carries no information. Saying “the table is 13 long” is

m as e
l
as vague as saying “the bag costs 50” without saying rupees.

m .co a g
l a se
a g
But why should the number be different?
s
Q2

m a
em
.co agl
a s
agl are of different sizes. When the five friends placed their

Because the handspans themselves
spread-out hands side by side, they found their handspans were not equal — and that is the

co m
.
whole reason.

se m
o m g l a
m .c of the table = (number of handspans) × (length of one handspan)
a
ase
Length

agl
Table length is the same for everyone.

∴ number of handspans is large when the handspan is small.
se m
com g l a
m . a
ase
agl
Reading Table 5.1 backwards therefore ranks their hands:

STUDENT NUMBER OF HANDSPANS SO THE HANDSPAN IS…

co m
m .
e
Tasneem Slightly less than 13 The largest of the five

com g l as
.Padma a
em
13 Next largest

a s
agl Anish Slightly more than 13 Middle

.c
s e m
m a
agl
Deepa

co
Between 13 and 14 Small

m .
e
las
Hardeep 14 The smallest of the five

ag

co m
m .
m ase
.co


a g l Page 4 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

A second, smaller reason is that even one person does not stretch the hand exactly the same
way each time, and a little gap or overlap creeps in at every step.

The lesson: a unit taken from the body — handspan, foot, cubit (haath), angula —
changes from person to person. So we need a unit for which measurements of the
same length made by different people do not differ. Such a unit is called a
standard unit, and that is exactly what Section 5.2 introduces.

Check it yourself: Measure the width of your classroom door in your handspans,
then ask your teacher to do it. Write both numbers on the board. Then measure it
with a metre scale — that number will be the same for both of you.

In-text Questions — Pages 83 & 84
5.2 Standard Units

Q1 Would it be convenient to use the unit metre to measure larger lengths, such as the
length of a railway track between two cities, or to measure smaller lengths, such as
the thickness of a page of a book?

No, it would not be convenient in either case. The metre is the right size for everyday objects
such as a room or a piece of cloth, but it is far too small for a railway line and far too big for a
page.
Case 1 — a railway track between two cities. The Delhi–Mumbai railway line is about 1384 km
long.

1 km = 1000 m (conversion factor)

1384 km = 1384 × 1000 m = 13,84,000 m

A number with seven digits is clumsy to say, to write and to compare. Written as 1384 km it is
instantly understood — which is why we use the kilometre for long distances.
Case 2 — the thickness of a page of a book. One page is about 0.1 mm thick.

Page 5 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

1 m = 100 cm and 1 cm = 10 mm

∴ 1 m = 100 × 10 mm = 1000 mm

So 1 mm = 1/1000 m = 0.001 m
Thickness of a page ≈ 0.1 mm = 0.1 × 0.001 m = 0.0001 m

A measurement written as 0.0001 m is hard to picture and easy to get wrong by a zero. Written
as 0.1 mm it is simple — which is why we use the millimetre for very small lengths.

TO MEASURE CONVENIENT UNIT TYPICAL VALUE

Railway track between two cities kilometre (km) ≈ 1384 km (Delhi–Mumbai)

Length of a cloth, height of a room metre (m) 2 m, 3 m

Length of a pencil centimetre (cm) ≈ 17 cm

Thickness of a page, of a coin millimetre (mm) 0.1 mm, 2 mm

Why it happens: a good unit is one that gives a small, easy number for the thing
being measured. That is the only reason km, m, cm and mm all exist — the length
itself never changes, only the way we write it. You would not measure milk in drops,
or a river in drops either.

Page 6 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Q2 Suppose we all measure the length of the table again, but this time using a metre
scale. Will our results still be different?

NAME OF THE STUDENT NUMBER OF HANDSPANS

Anish Slightly more than 13

Padma 13

Tasneem Slightly less than 13

Deepa Between 13 and 14

Hardeep 14

Table 5.1, page 81 — the length of the same table, measured by five children in their own
handspans.

No — this time everyone will get essentially the same answer, because the metre scale
carries a standard unit. One centimetre on Deepa's scale is exactly one centimetre on Hardeep's
scale, whereas one handspan was different for each of them.
If the table is, say, 1.24 m long, then every one of the five friends should get:

Length = 1.24 m

= 1.24 × 100 cm = 124 cm (using 1 m = 100 cm)

= 124 × 10 mm = 1240 mm (using 1 cm = 10 mm)

But — and this is what Padma's friend replies in the book — tiny differences of one or two
millimetres can still appear, and they have nothing to do with the unit. They come from
careless handling of the scale:

keeping the scale away from the table instead of touching it;
not laying the scale along the length of the table;
looking at the mark from the side instead of from directly above;
losing or gaining a millimetre each time the scale is lifted and shifted along a long table.

That is why the very next thing to learn is the correct way of using a scale.

Page 7 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Why it happens: a standard unit removes the large disagreement (13 versus 14).
Careful technique removes the small disagreement (124.0 cm versus 124.2 cm). You
need both to get a trustworthy measurement.

Tip: For a table longer than your scale, mark the point where the scale ends with a
pencil, then start the next measurement exactly from that mark. Adding up 100 cm +
24 cm gives 124 cm.

In-text Questions — Pages 84 & 85
5.3 Correct Way of Measuring Length

Q1 What is the correct way to place the scale?

Place the scale in contact with the object, along its length, with the marked edge of the
scale touching the object and the zero mark exactly against one end of it (Fig. 5.4a).

(a) Correct (b) Incorrect

0 5 10 15 0 5 10 15

Scale touches the object, Object held above the scale
0 mark at one end and tilted — reading is wrong

Method of placing the scale (as in Fig. 5.4). In (a) the object rests on the scale, along its length,
starting at 0. In (b) it is held above the scale and tilted, so the reading is too large.

The three rules:

1. Contact — the object must actually touch the scale. A gap between them makes you read
the mark from a slant.
2. Along the length — the scale must lie in the same direction as the object being measured,
not crossing it at an angle. A slanted scale always gives a length that is too large.
3. Zero at one end — line up the 0 mark with one end of the object and read the mark at the
other end.

Page 8 of 65

as e
Class 6 Science Chapter 5 Measurement of Length and Motion
a g l AglaSem · NCERT Solutions

co m
m.
Why a tilt makes it too large: the slanting line between the two ends of the object

m l a se
is longer than the straight one, just as a slanting path across a field is longer than
o
.c g your reading.
across. So every degree of tilt adds a little extraato
m
walking straight

l a se
g
aTip: Many plastic scales have a thin white margin before the 0 mark. Use the 0 mark,

co m
ag
never the physical edge of the plastic.
m .
as e
a g l
What is the correct position of the eye while reading the scale?
m
Q2

co
se m.
o m l a
.c be directly above the mark being read — position Baing Fig. 5.5. From the

The eyem
se positions A and C the same pencil tip appears to fall against a different mark, and the
must
l a
agreading is wrong.
slanting

m a s
m .co agl
l a se A B C
a g

co m
m .
m as e
.co a g l
se m
g l a
a 0 5 10 15

se m
c o m cm
A reads about 11.7. cm — too much g l a
em— correct a
B reads 11.0scm
l a C reads about 10.3 cm — too
ag little

co m
.
Correct position of the eye is ‘B’. From A the tip seems to fall to the right of the true mark, from C it

em
as
seems to fall to the left.
m l
.co a g
a s emWhat goes wrong at A and C: the pencil lies a little above the plane of the markings. When you
agl look from a slant, your line of sight travels on past the tip and meets the scale at a different
.c
mark. This error is called parallax.
s e m
m a
e m . co agl
g l as
a

co m
m .
m as e
.co


a g l Page 9 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Eye at A (to the left) → line of sight continues to the right → reading is too large

Eye at B (directly above) → line of sight is vertical → reading is correct

Eye at C (to the right) → line of sight continues to the left → reading is too small

Why only B works: only a vertical line of sight joins the tip and the mark that is truly
beneath it. Any other line passes through the tip and lands somewhere else, and the
error grows the more you lean.

Check it yourself: Hold a pencil on a scale and read its tip with your head straight
above it. Now, without moving the pencil, move your head 20 cm to the left and read
again. The reading changes even though nothing was touched — that is parallax.

Q3 How to measure the length if the ends of the scale are broken?

A broken scale can still be used. Do not try to guess where 0 was. Instead, line up one end of
the object with any clear full mark — say 1.0 cm — read the mark at the other end, and
subtract.

length = 9.4 cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
cm
0 mark broken off
reading 1.0 cm reading 10.4 cm

Correct method of placing a scale with a broken end (as in Fig. 5.6). One end of the object is at 1.0 cm
and the other at 10.4 cm.

Page 10 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Reading at the second end = 10.4 cm

Reading at the first end = 1.0 cm

Length of the object = 10.4 cm − 1.0 cm = 9.4 cm
In millimetres: 9.4 cm × 10 mm/cm = 94 mm

Why subtraction works: the numbers on a scale are distances measured from the 0
mark. So 10.4 cm and 1.0 cm are both distances from the same starting point, and
the gap between them is simply the difference. The broken piece never enters the
calculation.

Tip: Always start from a full centimetre mark such as 1.0 cm or 2.0 cm, not from 1.3
cm. Subtracting a whole number is quicker and you are far less likely to slip.

Q4 How do visually challenged students measure lengths?

They use scales whose markings are raised, so that the divisions can be felt with the
fingertips instead of being seen.

Tactile (embossed) scales — the centimetre and millimetre lines stand up above the
surface, and the numbers are printed in Braille beside them.
Notched metal rules — small notches or studs are cut at every centimetre, with a deeper
notch at every fifth or tenth mark, so the fingers can count quickly.
Click measuring tapes — the tape gives a small click or catch at every centimetre as it is
pulled out.
Talking instruments — modern digital tapes and laser distance meters announce the
reading aloud.

The unit does not change. A tactile scale measures in the same centimetres and millimetres as
an ordinary scale; only the way the reading reaches the person is different — through touch or
sound instead of sight.

The idea behind it: a measuring instrument has two jobs — to hold a set of fixed
marks, and to pass those marks on to the user. Braille and raised markings change
only the second job, so the measurement stays exactly as accurate.

Page 11 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Did you know? Braille itself is a system of raised dots, invented by Louis Braille
when he was only fifteen. Braille scales, protractors and even geometry kits are
made in India for schools.

Activity 5.1: Let us measure — Page 86
5.3 Correct Way of Measuring Length

ACTIVITY

Q1 Select some objects around you, such as a comb, a pen, a pencil, and an eraser to
measure their lengths. Measure their lengths one by one using a metre scale and
note down the measurements in Table 5.2.

OBJECT LENGTH OF THE OBJECT

Table 5.2, page 86 — the recording table to be filled in.

Method. Lay each object flat on the table. Put the metre scale beside it, touching it and along
its length, with the 0 mark exactly at one end. Bring your eye directly above the other end and
read the mark there.
Here is a completed Table 5.2 with the kind of values you will get. Measure your own objects —
your numbers will be a little different.

Page 12 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

OBJECT LENGTH OF THE OBJECT SAME LENGTH IN MM

Comb 15.5 cm 155 mm

Pen 13.8 cm 138 mm

Pencil 17.2 cm 172 mm

Eraser 4.3 cm 43 mm

Conversion used: 1 cm = 10 mm

15.5 cm × 10 mm/cm = 155 mm
4.3 cm × 10 mm/cm = 43 mm

Never forget the unit. Writing “15.5” alone tells nobody whether you mean centimetres, inches
or metres. A result must always have two parts — a number and a unit.

Tip: Leave a space between the number and the unit — write 15.5 cm, not 15.5cm.
Also write the symbols in small letters (cm, mm, m, km), never add an ‘s’ for the
plural, and do not put a full stop after them.

How to read the last digit: your 15-cm scale has 10 small divisions in each
centimetre, so the smallest length it can measure is 1 mm = 0.1 cm. That is why
every reading is written to one decimal place in cm — 15.5 cm, not just 15 cm or
15.53 cm.

Q2 Some of your friends in the class would have measured the length of the same
objects. Compare the lengths measured by you with that of your friends. Are the
measured lengths the same or slightly different? If not the same, discuss the
possible reasons for the differences.

The lengths will be almost the same — usually agreeing to within 1 mm or 2 mm. This is a
huge improvement on the handspan measurements of Section 5.1, where the answers differed
by a whole unit.

Page 13 of 65

as e
a
Class 6 Science Chapter 5 Measurement of Length and Motion
g l AglaSem · NCERT Solutions

co m
m.
OBJECT YOU FRIEND 1 FRIEND 2 SPREAD

m 17.2 cm l a scme = 2 mm
.co ag
Pencil 17.1 cm 17.3 cm 0.2

se m
g l a
Eraser
a
4.3 cm 4.3 cm 4.4 cm 0.1 cm = 1 mm

Possible reasons for the small differences:

co m
em .
1. Eye not directly above the mark — the parallax error of Fig. 5.5. This is the commonest ag
cause.
g l as
a
2. Scale not touching the object, or not laid along its length; a tilt always makes the reading

m
larger.

co
m.
3. Zero not aligned — starting from the plastic edge of the scale instead of the 0 mark.

o m l a se
4. Worn or broken end of an old scale, where the first millimetre is rubbed off.
g rounds it down. The
.c falls between two marks — one student rounds it up, aanother
m
se cannot measure less than 1 mm, so this is a genuine limit.
5. The end

g l ascale
a 6. The object itself — a comb with a slightly bent tooth or a pencil that has been sharpened
s
between the two measurements really has a different length.
m a
em
.co agl
a s
gl fixed the big problem; careful technique shrinks
The important conclusion: the differences are now small and random, not large
and systematic. A standardaunit
what is left. No measurement is ever perfectly exact — every instrument has a

com
.
smallest division below which it cannot go.

se m
o m l a
g each time, and write all
m .cThis: Measure the same pencil five times, lifting the scale
a
asefive readings. Take the middle value. Repeating a measurement and taking the
Try

agl average is exactly what scientists do to reduce such errors.
se m
com g l a
m . a
ase
Q3
agl
Why are some length measuring devices made up of flexible materials?

co m
m .
o m l a se
Because many things we need to measure are not straight. A stiff scale can only lie along a
g tape bends and hugs the
.c line, so it simply cannot follow a curved surface. A flexible
a
m
se curve, and its markings stay the same length while it bends.
straight

a
agl c
m .
m a s e
e m . co agl
g l as
a

com
m .
m ase
.co


a g l Page 14 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

WHAT IS BEING MEASURED SHAPE INSTRUMENT THAT WORKS

Length of a pencil Straight 15-cm scale

Height of a room Straight but long Metre scale or tape

Chest, waist, sleeve of a shirt Curved (round the body) Tailor's flexible tape

Girth of a tree trunk Curved Flexible tape or a thread

Head size for a helmet Curved Flexible tape

A flexible tape is also easy to roll up, so a 3 m or 30 m tape fits in a pocket, while a 3 m rigid rod
would be impossible to carry to a Kabaddi ground.

The one condition: the material must bend but must not stretch. A tailor's tape is
made of coated cloth or fibreglass, and a carpenter's tape of thin spring steel —
both bend freely but keep their length. A rubber band would also bend, but it
stretches, so every reading would be too small. That is exactly why Tasneem must
not use stretchable rubber for her metre scale (Question 12).

Check it yourself: Wrap a thread once around your wrist, mark the point where it
meets, straighten the thread on a 15-cm scale and read the length. You have just
measured a curve with a straight scale.

In-text Questions — Page 87

Page 15 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

5.4 Measuring the Length of a Curved Line

Q1 Anish and his parents fixed electric string lights on the arches of the verandah of
their house, as shown in Fig. 5.7, for a celebration at home. How would they have
measured the required length of string lights?

electric string lights

three arches of the verandah

Fig. 5.7, page 87 — redrawn sketch: the verandah of Anish’s house, with a string of lights
running along the curve of each arch and along the top.

The arches are curved, so a stiff metre scale is of no use. They would have measured the curve
with a thread (or with a flexible measuring tape), and then straightened the thread along a
metre scale.
The thread method, step by step:

1. Tie a knot at one end of the thread and hold it at the starting point of the first arch.
2. Press the thread along the arch with your fingers so that it follows the curve exactly, without
stretching it and without leaving it slack (Fig. 5.8).
3. Mark the thread with a pen at the point where the arch ends.
4. Straighten the thread on a table and measure the marked portion with a metre scale.
5. Repeat for each arch and add up the lengths.

A worked example. Suppose the verandah has 3 arches and the thread for one arch measures
2 m 40 cm:

Page 16 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Length of one arch = 2 m 40 cm = 2.40 m

Number of arches = 3

Total = 3 × 2.40 m = 7.20 m

In centimetres: 7.20 m × 100 cm/m = 720 cm

Adding about 10% extra for the drooping and for joining = 7.20 m + 0.72 m ≈ 8 m of string

lights

Why the thread works: the thread takes the shape of the curve, so the length of
thread used is the length of the curve. Straightening it does not change how much
thread there is — it only turns a curved length into a straight one that a scale can
read.

Tip: Use a thread that does not stretch — cotton or jute, not elastic or nylon fishing
line. If the thread stretches while you press it along the arch, your answer will be too
large and you will buy more lights than you need.

In-text Questions — Pages 87 & 88
5.5 Describing Position

Q1 Tasneem and Padma say that the garden would be closer, while Deepa and Anish
feel that the school would be closer, Hardeep thinks that both would be almost at
an equal distance. Who do you think is correct?

All of them are correct. Nobody has made a mistake — each child is simply judging the
distance from his or her own house, and the houses are at different places along the road.

Page 17 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Bus stand Deepa Hardeep Padma
School Anish Tasneem Garden

Deepa and Anish live nearer the school · Tasneem and Padma live nearer the garden
Hardeep lives almost midway — so everyone is right

Location of the bus stand, the school, the garden and the houses of Deepa and her friends (as in Fig.
5.9).

CHILD WHERE THE HOUSE IS WHAT THEY SAY CORRECT?

Deepa, Anish Nearer the school end of the road School is closer Yes

Hardeep About midway between the two Both are almost equally far Yes

Tasneem, Padma Nearer the garden end of the road Garden is closer Yes

Why it happens: a distance is never “just a distance”. It is always a distance from
something. Five different starting points give five different — and equally true —
answers.

Q2 Then, why are their observations different?

Because each of them is using a different reference point — his or her own house. The
school and the garden never moved; only the point from which the distances were judged
changed.
The moment they all agree to measure from one common point, say the bus stand, their
observations become identical:

Page 18 of 65

as e
a
Class 6 Science Chapter 5 Measurement of Length and Motion
g l AglaSem · NCERT Solutions

co m
m.
MEASURED DISTANCE TO THE DISTANCE TO THE WHICH IS NEARER?

as e
com
FROM SCHOOL GARDEN

. a g l
m
ase
Padma's house Large Small Garden

gl house
aDeepa's Small Large School

m
.co ag
Bus stand Small Large School — for every one

sem
(common) of them

a
agl
This gives the definition the chapter is building towards:

co m
When distance is stated with respect to a fixed object or point,
e m.
m l as
m .co
that point is called a reference point.
a g
l a se
a g
Why a reference point is compulsory: without it a statement like “the garden is far”
m a s
c o agl
cannot be checked by anyone else. With it — “the garden is 2 km from the bus stand”
.
msame answer. This is the same idea as a
s e
— every person in the class gets the
a instead of to length.
agl
standard unit, applied to position

. com
Try This: Ask three classmates how far the school gate is from “here”. Then ask them

m a s
how far it is from the school flag post. The first set of answers willemdiffer; the second
o agree.
set.cwill
a gl
a s em
agl
se m
In-text Questions — Page 89
com g l a
m . a
ase
5.5 Describing Position

agl
Q1 What do such kilometre stones indicate? How could Padma conclude that she was

co m
.
getting closer to her destination?

em
m l as
.co a g
emA kilometre stone shows the distance of that spot from a named place — here, from Delhi.

a s
agl Delhi is the reference point, and the number on the stone is Padma's position with respect to
.c
it.
s e m
m a
e m . co agl
g l as
a

com
m .
m ase
.co


a g l Page 19 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

70 km → 60 km : the number falls, so the bus is getting closer
Padma starts here

0 10 20 30 40 50 60 70

DELHI
reference point
All distances are measured in km from Delhi

Positions of kilometre stones with respect to Delhi as a reference point (as in Fig. 5.13).

How Padma could tell she was getting closer: she compared two readings taken at two
different times.

Earlier stone: position = 70 km from Delhi

Later stone: position = 60 km from Delhi
Distance covered between the two stones = 70 km − 60 km = 10 km

The number is getting smaller ⇒ the bus is moving towards Delhi.

Had the numbers been rising — 60 km, 70 km, 80 km — she would have known the bus was
moving away from Delhi.

Why it happens: a kilometre stone does not measure how far the bus has travelled
from home. It measures the gap between the bus and the reference point. When
that gap shrinks with time, the bus is approaching; when it grows, the bus is
receding.

Did you know? The colour of the top of an Indian milestone tells you the kind of
road — yellow for a National Highway, green for a State Highway, black or blue for
a district or city road, and orange for a village road built under Pradhan Mantri
Gram Sadak Yojana.

Page 20 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Q2 Does this mean that the position of Padma, with respect to the reference point, is
changing with time? When does the position of an object change with respect to a
reference point? Does it change when an object is moving?

Yes to all three. Take them one at a time.
(i) Is Padma's position changing with time? Yes. At one moment she was 70 km from Delhi; a
little later she was 60 km from Delhi. The reference point (Delhi) did not move, the road did not
move — only Padma did. So her position with respect to Delhi is changing as time passes.
(ii) When does the position of an object change with respect to a reference point? Only
when the gap between the object and that point changes. That happens when the object
moves nearer or farther, and it is measured by comparing readings at two different times.

Position at time 1 = 70 km from Delhi

Position at time 2 = 60 km from Delhi
Change of position = 10 km, towards Delhi

(iii) Does it change when an object is moving? Yes — and this is exactly how motion is defined
in the very next section:

An object is said to be in motion if its position changes with respect to the reference point

with time.

If the position does not change with time, the object is said to be at rest.

One careful point: the object must move relative to the chosen reference point. If
Padma's bag is on the seat beside her, it is at rest with respect to Padma even
though both are speeding along the highway — because the gap between Padma
and her bag never changes. Motion and rest always depend on which reference
point you pick.

Tip: Two readings are always needed to decide motion — one position is never
enough. “70 km from Delhi” alone tells you where she is, not whether she is moving.

Activity 5.2: Let us explore — Page 90

Page 21 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

5.6 Moving Things

ACTIVITY

Q1 Look around and prepare a list of five objects that are in motion and five objects
that are at rest. Record your observations in Table 5.3. Think about how you decided
whether an object was in motion or at rest. Write your explanation (justification) in
Table 5.3.

OBJECTS IN MOTION JUSTIFICATION OBJECTS AT JUSTIFICATION
REST

Cow grazing in the Tree
field

Table 5.3, page 90 — the recording table; the first row is already filled in as an example.

Choose a reference point first — for a classroom activity, the school building or the ground is
convenient — and then look at each object twice, a minute apart.

Page 22 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

OBJECTS IN JUSTIFICATION OBJECTS AT JUSTIFICATION
MOTION REST

Cow grazing in the It is at a different spot in the field a Tree Its distance from the school
field minute later wall never changes

Bus on the road It has gone past the bus stop by the Blackboard It stays on the same wall at the
time we look again same height

Blades of a A mark on one blade keeps returning School bench It is at the same place in the
running fan to a new position each instant room after a minute

Boy running in the His distance from the goal post is Electric pole Its distance from the gate is
playground decreasing always the same

Water flowing in a A floating leaf is carried further along Water in a The surface stays where it is
drain bucket

How the decision was taken, in words: note where the object is with respect to the reference
point, wait for some time, then look again. If it is now at a different distance or direction, it is
in motion; if it is exactly where it was, it is at rest.

Why the reference point must be stated: the same object can appear on both lists.
A passenger sitting in a moving bus is at rest with respect to the bus, but in motion
with respect to a building on the roadside. Without naming the reference point,
neither answer is right or wrong.

Try This: Write your five moving objects again, but this time choose the Sun as the
reference point. Now even the tree and the electric pole are in motion, because the
whole Earth is carrying them around the Sun.

Q2 Compare and analyse your justifications. How can one decide if an object is in
motion or at rest?

Read through everybody's justifications and one pattern appears in every single one: each of
them mentions a fixed point and a gap of time.

Page 23 of 65

as e
a
Class 6 Science Chapter 5 Measurement of Length and Motion
g l AglaSem · NCERT Solutions

co m
e m.
Step 1 — Choose a reference point (a wall, a pole, a building).
m l as
.co
Step 2 — Note the position of the object with respect to it at one time.
m a g
l a se
g
Step 3 — Note the position again after some time.
aStep 4 — Position changed ⇒ the object is in motion.

com
. ag
Position unchanged ⇒ the object is at rest.
e m
g l as
In the textbook's own words: a
m
An object is said to be in motion if its position changes with respect to the reference
co
m.
point with time.

as e
ombe at rest. l
If an object is not changing its position with respect to the reference point with time, it
is said.cto a g
m
ase
aginl their seats, so with the bus as the reference point they are at rest. But looking out of the
Deepa's bus is the perfect test case. All the passengers are seated. A minute later they are still

m a s
agl
window, the trees and poles slide past — so with a building outside as the reference point, the
same passengers are in motion.
m.co
l a se
a g
Why both answers are correct: motion is not a property that an object owns by
itself. It is a relation between the object and a reference point. Change the
co m
reference point and the answer legitimately changes. That is why a scientist always
m .
m as e
l
says “in motion with respect to…”.

m .co a g
l a se
ag
Think it over! — Page 91
se m
com g l a
. a
5.6 Moving Things
m
ase
agl
THINK IT OVER!

Q1 Suppose you are travelling on a ship which is moving at a constant speed along a
co m
m
straight line on a calm sea. Suppose there is no window on the ship. Is there any.
m as e
.co l
way that you can determine whether the ship is moving or is stationary?
a g
a s emANSWER
agl
.c
m
No. Shut inside the cabin, there is no experiment you can perform that will tell you

m a s e
co agl
whether the ship is moving or standing still — provided the speed really is constant, the path

m .
e
really is straight and the sea really is calm.

g l as
Why not? Everything inside the cabin — you, the floor, the air, a glass of water — is moving
a
together with the ship at exactly the same speed. So the position of each of these things with

m
respect to the ship never changes, and the ship is the only reference point you have left.

. co
e m
m l as
.co a g
Page 24 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

TEST YOU MIGHT TRY SHIP STANDING SHIP MOVING STEADILY
STILL

Drop a coin from your hand Falls straight down at your Falls straight down at your feet — same
feet result

Pour water into a glass Falls straight into the glass Falls straight into the glass — same result

Throw a ball up and catch it Comes back to your hand Comes back to your hand — same result

Look at the water surface in a Flat and level Flat and level — same result
bowl

When you can tell. The moment the motion stops being steady and straight, your body feels it
at once:

the ship speeds up or slows down — you are pushed backwards or forwards;
the ship turns — you lean to one side, and hanging objects swing;
the sea is rough — the cabin rolls and pitches;
you open a window — now the sea and the shore are available as an outside reference
point, and the answer becomes obvious.

The big idea: steady motion in a straight line cannot be detected from inside. This is
why you can read a book comfortably in a train running smoothly at 100 km/h, but
the same book slides off your lap when the train brakes. Galileo described exactly
this puzzle — using a ship, just as your textbook does — about four hundred years
ago.

Did you know? This is also why we do not feel the Earth's motion. The Earth carries
us around the Sun at roughly 30 km every second, but it does so smoothly, and
everything around us — air, buildings, clouds — travels along with us.

Activity 5.3: Let us explore — Pages 91 & 92

Page 25 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

5.7 Types of Motion

ACTIVITY

Q1 Take an eraser and drop it from a certain height. Observe its motion. Does it move
along a straight line?

Yes. Once you let go, the eraser falls straight down along a vertical line until it hits the floor. Its
path is a straight line, so this is linear motion.

When an object moves along a straight line,

its motion is called linear motion.

What to observe carefully: hold the eraser still, then simply open your fingers — do not throw
it sideways. Watch the path from the side. It goes straight down, and it lands directly below the
point from which it was released.

Why it falls straight: the Earth pulls every object straight down towards its centre. If
nothing pushes the eraser sideways, there is no reason for it to drift left or right, so
the path stays a straight vertical line. (Notice that the speed increases as it falls —
but the type of motion is decided by the shape of the path, not by the speed.)

Try This: Drop the eraser and, at the same instant, throw a second eraser sideways
from the same height. The dropped one moves in a straight line; the thrown one
follows a curved path. Only the first is linear motion.

Q2 When an orange drops from the tree, does it move in a straight line?

Yes. An orange that becomes ripe and separates from its stalk falls vertically downwards in a
straight line, exactly like the eraser. It is another example of linear motion.
Two things to notice:

The orange lands almost directly below the branch it hung from — proof that the path was
vertical.
It moves faster and faster as it comes down, but that does not change the type of motion.
Linear motion only means the path is a straight line.

Page 26 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

When it would not be a straight line: if a strong wind blows, or if a bird or a boy's
stone knocks the orange sideways, it gets a sideways push as well as the downward
pull, and the path curves. In still air, though, the fall is straight.

Did you know? A story of exactly this kind — an apple falling from a tree — is said to
have set Isaac Newton thinking about why objects always fall towards the Earth.

Q3 Have you seen the Republic Day parade? Recall the march-past of students during
the parade. Do they move on a straight-line path?

Yes. During the march-past on Kartavya Path the contingents move in straight lines — that is
the whole point of the drill. Each row keeps its line, each student keeps a fixed distance from the
one in front, and the entire block slides forward along a straight path. This is linear motion.

PART OF THE PARADE PATH TYPE OF MOTION

Students marching down the road Straight line Linear motion

The whole contingent turning a corner Curved (an arc) Not linear

A marcher's arms swinging front and back To and fro about the shoulder Oscillatory motion

Wheels of the tableaux (jhankis) Round and round Circular motion

Why the drill insists on it: a straight-line path is the only one on which every
marcher in a row covers the same distance in the same time. On a curve, the
marcher on the outside would have to walk further and the line would break. That is
why contingents slow down and change step while turning.

Look for it: the same picture in the book shows a heavy box being pushed across
the floor (Fig. 5.14) — another everyday case of linear motion.

Page 27 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Q4 When an object moves along a straight line, its motion is called linear motion.
Identify such linear motion in your surroundings.

Linear motion is everywhere once you start looking for a straight-line path.

EXAMPLE AROUND YOU WHY IT IS LINEAR MOTION

A car or bus on a straight road The whole vehicle travels along a straight path

A lift going up or down its shaft Vertical straight-line path between floors

A heavy box being pushed across the floor Slides straight in the direction of the push

An athlete running the 100 m race Straight track from start to finish

A ball rolling down a straight ramp Path is a straight slope

A drawer being pulled out of a table Moves straight out along its rails

Rain falling on a still day Each drop falls along a vertical straight line

A train on a straight stretch of track Rails keep it exactly on a straight path

A useful caution: a bicycle going straight down a road shows linear motion as a
whole, but its wheels are in circular motion at the same time, and the pedals go
round in circles too. One machine can show more than one type of motion at once —
always say which part you are talking about.

Q5 But do things always move along a straight line? You might have enjoyed playing
on swings and merry-go-rounds. Are these types of motion also linear motion?

No. Neither of them is linear motion, because in neither case is the path a straight line.

RIDE SHAPE OF THE PATH TYPE OF MOTION

Merry-go-round A complete circle, round and round the central pole Circular motion

Swing A short arc, forward and back over the same path Oscillatory motion

Page 28 of 65

as e
a
Class 6 Science Chapter 5 Measurement of Length and Motion
g l AglaSem · NCERT Solutions

Notice the difference between the two. The merry-go-round keeps going the same way round
co m
and completes circle after circle. The swing comes back along the same arc — forward, back,
e m.
m l as
.co g
forward, back — about a fixed lowest position.

em a
a s
gl is a straight line → linear motion
aPath
m
Path is a circle → circular motion
. co ag
em
Path is to and fro about a fixed position → oscillatory motion

g l as
a
Why the type of motion matters: the name is decided entirely by the shape of the

co m
m.
path, never by speed and never by what the object is. A slow car and a fast car on a

as e
com l
straight road are both in linear motion; a slow fan and a fast fan are both in circular
. a g
em
motion.

a s
a gl
Tip: When you are unsure, trace the path with your finger in the air. If your finger

a s
com agl
comes back over the same short path, it is oscillatory. If it keeps going round, it is
.
a s em
circular. If it goes straight on, it is linear.

agl

co m
Activity 5.4: Let us investigate — Page 92
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 29 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

5.7 Types of Motion

ACTIVITY

Q1 Tie an eraser (or a potato) to one end of a thread. Hold the other end of the thread
with your hand and whirl it (Fig. 5.15). Observe its motion. Is the motion of the
eraser the same as that of a merry-go-round?

eraser tied to a thread

circular path

merry-go-round

Fig. 5.15, page 93 — redrawn sketch: an eraser whirled on a thread, and a merry-go-
round. Both travel along a circular path.

Yes — the two are the same kind of motion. The eraser goes round and round along a
circular path, and so does a child sitting on a merry-go-round. Both are examples of circular
motion.

When an object moves along a circular path,

its motion is called circular motion.

Page 30 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

WHIRLING ERASER MERRY-GO-ROUND

Centre of the circle Your hand The central pole

What keeps it on the The thread pulls it inward The metal arms pull the seat inward
circle

Distance from the centre Always the same (the length of the Always the same (the length of the
thread) arm)

Path traced A circle, repeated again and again A circle, repeated again and again

The key test for circular motion: the moving object stays at a constant distance
from one fixed point. Measure the thread — say 40 cm — and the eraser is 40 cm
from your hand at every instant of the whirl. That is exactly what makes the path a
circle.

Check it yourself: While whirling, let go of the thread (do it outdoors, away from
people and windows). The eraser flies off in a straight line, not in a circle — proof
that it was the pull of the thread that was bending its path into a circle all along.

Activity 5.5: Let us investigate — Page 93

Page 31 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

5.7 Types of Motion

ACTIVITY

Q1 Tie an eraser (or a potato) to one end of a thread. Hang the eraser by holding the
other end of the thread (Fig. 5.16). Keep your hand steady. Using the other hand,
take the eraser slightly to one side and then release. Does it start moving to and
fro? Is its motion similar to the motion of a swing?

hold the hand steady

the eraser swings to and fro swing in a park

Fig. 5.16, page 93 — redrawn sketch: an eraser hanging from a thread swings to and fro,
just like a swing.

Yes to both. The eraser swings to and fro about the lowest position, and its motion is exactly
like a swing in a park. This is oscillatory motion.

When an object moves to and fro about some fixed position,

its motion is called oscillatory motion.

What you will see:

The eraser passes through the same lowest point every time — that is the fixed position it
oscillates about.
It repeats its path over and over: right, lowest point, left, lowest point, right…
Each complete to-and-fro trip takes the same time, so the motion is also periodic.
The swings become smaller and smaller and finally stop, because air resistance and friction
at the top slowly take away its motion.

Page 32 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

HANGING ERASER SWING IN A PARK

Fixed point at the top Your steady hand The bar of the swing frame

What moves The eraser at the end of the thread The seat with the child on it

Path A short arc, repeated to and fro A short arc, repeated to and fro

Why your hand must be steady: the oscillation is measured about a fixed position.
If your hand wanders, the lowest point wanders too, and you no longer have a clean
to-and-fro motion to observe. The same is true of a wall-clock pendulum — the clock
case holds the top absolutely still.

Try This: Count how many complete to-and-fro trips the eraser makes in 30 seconds
with a 30 cm thread, and then with a 60 cm thread. The longer thread gives fewer
trips — the very fact that makes a pendulum useful for keeping time.

Activity 5.6: Let us investigate — Page 94

Page 33 of 65

as e
a
Class 6 Science Chapter 5 Measurement of Length and Motion
g l AglaSem · NCERT Solutions

5.7 Types of Motion
co m
e m.
m as
ACTIVITY

.co a g l
a s ema thin metal strip of about 50 cm long. Hold its one end pressed to a table. You
gl
Take
a
Q1
may use a few books or a brick to hold it (Fig. 5.17). Press the free end of the strip
slightly and let it go. Observe the motion of this end of the strip. Does it move up

com
. ag
and down?
e m
g l as
a

co m
em.
as
a few books (or a brick)
m l
m .co a g
l a se
ag thin metal strip

m a s
table
m.co agl
l a se
a g free end moves up and down

co m
m .
o m l a se on the table under
.c ag
Fig. 5.17, page 94 — redrawn sketch: one end of the strip is pressed

a s em some books; the free end springs up and down.

agl
se m
com g l a
m . a
ase
agl
Yes. The free end springs up and down about its original straight position, very fast at first and
then more and more gently until it stops. This is also oscillatory motion.

co m
The strip moves to and fro about a fixed position (its resting level).
m .
m as e
.co
∴ its motion is oscillatory motion.
a g l
a s em
agl Compare it with the hanging eraser of Activity 5.5:
.c
s e m
m a
e m . co agl
g l as
a

com
m .
m ase
.co


a g l Page 34 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

HANGING ERASER METAL STRIP

Direction of the to-and-fro motion Sideways (left–right) Up and down

Fixed position it moves about The lowest point of the arc The level at which the strip rests

What brings it back each time The pull of the Earth The springiness of the metal

Type of motion Oscillatory Oscillatory

Why up-and-down still counts: the definition says nothing about direction. Any
repeated to-and-fro motion about a fixed position is oscillatory — sideways like a
swing, up and down like this strip, or in and out like the skin of a drum.

Did you know? If you press the strip only a little and let it go, it oscillates so fast that
you hear it as a low buzz. Every sound you hear is produced by something oscillating
— a strip, a string, a drumhead, or your own vocal cords.

Activity 5.7: Let us identify — Pages 94 & 95

Page 35 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

5.7 Types of Motion

ACTIVITY

Q1 Look at the picture of a children’s park (Fig. 5.18) or visit a children’s park. Observe
different kinds of motions. Classify them as linear, circular or oscillatory motion.
List them in Table 5.4. Give your justification for why you put each in a certain
category.

Slide Merry-go-round Swing

See-saw Skipping rope Monkey bars

Fig. 5.18, page 95 — redrawn sketch of the children’s park: the six things whose motion
you have to classify.

OBJECT LINEAR MOTION CIRCULAR MOTION OSCILLATORY MOTION

Swing Moving to and fro

Table 5.4, page 95 — the classification table; the swing is filled in as an example.

Page 36 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Look at the path each thing traces, and the answer follows at once.

straight path

Linear motion Circular motion

Oscillatory motion

The three types of motion: a straight-line path, a circular path, and a to-and-fro path about a fixed
position.

Table 5.4: Types of Motion

OBJECT LINEAR CIRCULAR MOTION OSCILLATORY MOTION
MOTION

Swing Moving to and fro

See-saw Each end goes up and down
about the middle support

Merry-go-round Goes round and round
the central pole

Child sliding down the Slides along the
slide straight slope of the
slide

Child climbing the Moves straight up,
ladder step by step

Skipping rope being The rope goes round and
turned round the child's hands

Child hanging and Body swings to and fro about
swinging on the the bar held
monkey bars

Page 37 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

How to justify each entry: name the path, not the object. “The see-saw is
oscillatory because each end repeatedly rises and falls about the fixed central
support” is a justification; “the see-saw is oscillatory because it is a see-saw” is not.

Tip: One object can appear in two columns. The skipping child moves up and down
(oscillatory) while the rope goes round and round (circular). Write the part you
mean.

Let us enhance our learning — Pages 97 & 98
Chapter exercises

LET US ENHANCE OUR LEARNING

Q1 Some lengths are given in Column I of Table 5.5. Some units are given in Column II.
Match the lengths with the units suitable for measuring those lengths.

COLUMN I COLUMN II

Distance between Delhi and Lucknow centimetre

Thickness of a coin kilometre

Length of an eraser metre

Length of school ground millimetre

Table 5.5, page 97 — as printed in the book. The two columns are not in matching order.

Pick the unit that gives a small, easy number for that length.

Page 38 of 65

as e
a
Class 6 Science Chapter 5 Measurement of Length and Motion
g l AglaSem · NCERT Solutions

co m
m.
COLUMN I MATCHES WITH TYPICAL WHY THIS UNIT

as e
com
(COLUMN II) VALUE

. a g l
s e m
Distance between Delhi kilometre ≈ 500 km In metres it would be 5,00,000 m
and a
a g l Lucknow — far too long a number

Thickness of a coin millimetre ≈ 2 mm In centimetres it is only 0.2 cm;

m
.co ag
mm gives a whole number

a sem
agl
Length of an eraser centimetre ≈ 4 cm Fits neatly on a 15-cm scale

Length of school metre ≈ 100 m In km it would be 0.1 km — an
ground awkward decimal
co m
e m.
comthe conversion factors: g l as
Check .with a
a s em
agl 500 km = 500 × 1000 m = 5,00,000 m (1 km = 1000 m)
s
2 mm = 2 × 0.1 cm = 0.2 cm (1 mm = 0.1 cm)
m a
m .co agl
se
100 m = 100 ÷ 1000 km = 0.1 km

g l a
a
The rule of thumb: choose the unit for which the number comes out roughly

co m
.
between 1 and 1000. That is why we say 500 km, not 5,00,000 m — and 2 mm, not
e m
m as
0.002 m.

.co a g l
sem
g l a
a
m
Read the following statements and mark True (T) or False (F) against each. (i) The
se
Q2

o m
motion of a car moving on a straight road is an example of linear motion. (ii) Any
l a
m .c with respect to a reference point with time is ag
sekm = 100 cm
object which is changing its position

l a
said to be in motion. (iii) 1
ag
m

. co
se m
com a
STATEMENT T/F

.(i) a g l
e m
as
The motion of a car moving on a straight road is an example of linear motion. True (T)

agl c
(ii)
.
Any object which is changing its position with respect to a reference point with time is said to be in True (T)

s e m
m a
motion.

e m . co agl
as
(iii) 1 km = 100 cm False

a g l (F)

co m
m .
m as e
.co


a g l Page 39 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

(i) True. The path of the car is a straight line, and motion along a straight line is by definition
linear motion.
(ii) True. This is exactly the definition of motion given on page 90 of your book — position
changing with respect to a reference point, with time.
(iii) False. Work the conversion out step by step:

1 km = 1000 m (conversion factor)

1 m = 100 cm (conversion factor)

∴ 1 km = 1000 × 100 cm

1 km = 1,00,000 cm (one lakh centimetres)

So the statement is wrong by a factor of 1000. The correct short statement is 1 m = 100 cm.

Where the mistake comes from: students remember “100” with centimetres and
attach it to the wrong unit. Fix the chain in your mind and you can never go wrong:
km → m is ×1000, m → cm is ×100, cm → mm is ×10.

Q3 Which of the following is not a standard unit of measuring length? (i) millimetre (ii)
centimetre (iii) kilometre (iv) handspan

Answer: (iv) handspan.

OPTION STANDARD? REASON

(i) millimetre Standard A fixed part of the metre; 1 mm = 0.1 cm everywhere in the world

(ii) Standard 1 m = 100 cm, the same for everyone
centimetre

(iii) Standard 1 km = 1000 m, the same for everyone
kilometre

(iv) Not standard Its size depends on whose hand it is — Deepa, Anish and Hardeep all got
handspan different numbers for the same table

Page 40 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

What makes a unit “standard”: a standard unit gives the same value no matter
who measures, where they measure, or when. mm, cm and km are all fixed parts of
the SI metre. A handspan is a body measurement, so it changes from person to
person — that is precisely why Table 5.1 gave five different answers.

Tip: Foot, cubit (haath), angula and stride are all in the same non-standard family as
the handspan, however useful they may be for a rough estimate.

Q4 Search for the different scales or measuring tapes at your home and school. Find
out the smallest value that can be measured using each of these scales. Record
your observations in a tabular form.

Method. On each instrument, find the gap between two neighbouring marks. That gap is the
smallest length the instrument can measure — it is called the least count.

Least count = distance between two big marks ÷ number of small divisions between them

On a 15-cm scale: 1 cm ÷ 10 = 0.1 cm = 1 mm

Here is a completed table. Fill in the instruments you actually find at home and at school.

SCALE / MEASURING TOTAL LENGTH IT CAN SMALLEST VALUE IT CAN
DEVICE MEASURE MEASURE

15-cm plastic scale (geometry 15 cm 1 mm = 0.1 cm
box)

30-cm plastic scale 30 cm 1 mm

Wooden metre scale 100 cm = 1 m 1 mm
(blackboard)

Tailor's cloth measuring tape 150 cm 1 mm (some show only 0.5 cm)

Steel measuring tape 3 m or 5 m 1 mm
(carpenter)

Long tape for the playground 30 m 1 cm

Tape printed only in 150 cm 1 cm
centimetres

Page 41 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Why the smallest value matters: you cannot report a length finer than the
instrument allows. With a 15-cm scale a pencil can be recorded as 17.2 cm but never
as 17.24 cm — the scale simply has no mark there. Notice also that the long 30 m
tape is coarser: instruments made for long distances usually have larger divisions.

Tip: Count the small divisions carefully. If there are 10 small gaps in 1 cm, the least
count is 1 mm; if there are only 2, it is 5 mm.

Q5 Suppose the distance between your school and home is 1.5 km. Express it in metres.

Use the conversion factor 1 km = 1000 m and multiply.

Distance = 1.5 km

1 km = 1000 m (conversion factor)

∴ 1.5 km = 1.5 × 1000 m

Distance = 1500 m

Check it another way. 1.5 km is 1 km and half a kilometre:

1 km = 1000 m

0.5 km = 1000 ÷ 2 = 500 m
Total = 1000 m + 500 m = 1500 m ✓

The same distance in other units:

UNIT WORKING VALUE

metre 1.5 × 1000 1500 m

centimetre 1500 × 100 1,50,000 cm

millimetre 1,50,000 × 10 15,00,000 mm

Page 42 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Why we multiply, not divide: the metre is smaller than the kilometre, so it takes
more of them to cover the same distance. Going from a bigger unit to a smaller unit,
the number always gets bigger.

Tip: A quick check — 1500 m is a number bigger than 1.5. If your answer had come
out as 0.0015, you would know at once you had divided by mistake.

Q6 Take a tumbler or a bottle. Measure the length of the curved part of the base of
glass or bottle and record it.

The base is a circle, so a stiff scale cannot be laid along it. Use the thread method of Fig. 5.8.
Steps:

1. Take a thread that does not stretch. Put a small ink mark near one end.
2. Wrap the thread exactly once around the base of the tumbler, keeping it snug but not
stretched.
3. Mark the thread at the point where it meets the first mark.
4. Take the thread off, straighten it on the table and measure the marked length with a 15-cm
or metre scale.
5. Repeat twice more and take the middle value.

A sample record (measure your own tumbler — the numbers will differ):

TRIAL LENGTH OF THREAD

1 21.9 cm

2 22.1 cm

3 22.0 cm

Recorded value 22.0 cm = 220 mm = 0.220 m

Cross-check using the width of the base:

Diameter of the base measured with a scale = 7.0 cm

Length round a circle = 3.14 × diameter

= 3.14 × 7.0 cm = 21.98 cm ≈ 22.0 cm ✓

Page 43 of 65

as e
a
Class 6 Science Chapter 5 Measurement of Length and Motion
g l AglaSem · NCERT Solutions

co m
m.
Why the thread must not stretch: a stretched thread needs more length to go

m l a se
round, so the reading comes out too large. Cotton or jute thread is ideal; a rubber
o
.c worst possible choice. a g
m
band is the

l a se
g
aTip: Wrap the thread only once round. If it accidentally goes round twice, you will

com
ag
get about 44 cm and must halve it.
m .
as e
a g l
Measure the height of your friend and express it in (i) metres (ii) centimetres and
m
Q7

co
m.
(iii) millimetres.

o m l a se
ANSWER c
. a g
m
se Ask your friend to stand straight against a wall, without shoes, heels touching the wall
l a
agand looking straight ahead. Place a book flat on the head, touching the wall, and mark the wall
Method.

s
along the lower edge of the book. Measure from the floor to the mark with a metre scale or a
m a
.co agl
measuring tape.

se m
Suppose the mark is at 142 cm. Then:
g l a
a
ASKED IN CONVERSION FACTOR USED WORKING ANSWER

co m 142 cm
m .
e
(ii) centimetres measured directly —

com g l as
. a
sem
(i) metres 1 m = 100 cm 142 ÷ 100 1.42 m

a (iii) millimetres
agl 1 cm = 10 mm 142 × 10 1420 mm

se m
com g l a
. a
em
Height = 142 cm
a s
agl
In metres: 142 cm ÷ 100 = 1.42 m

In millimetres: 142 cm × 10 = 1420 mm

co m
Check: 1.42 m × 1000 mm/m = 1420 mm ✓
m .
o m l a se
g 6 students are between 1.30 m
.c your friend and put your own number in. Most Class
a
se m
Measure
a
agl
and 1.55 m tall.

.c
s e m
m a
co agl
Note the direction of each conversion: cm → m goes to a bigger unit, so we

m .
e
divide and the number gets smaller (142 → 1.42). cm → mm goes to a smaller unit,

g l as
so we multiply and the number gets bigger (142 → 1420). The height itself never
changed. a

co m
m .
m ase
.co


a g l Page 44 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Tip: Keep the book horizontal. If it tilts, the mark goes too high and every one of
your three answers will be wrong together.

Q8 You are given a coin. Estimate how many coins are required to be placed one after
the other lengthwise, without leaving any gap between them, to cover the whole
length of the chosen side of a notebook. Verify your estimate by measuring the
same side of the notebook and the size of the coin using a 15-cm scale.

Step 1 — Estimate first. Look at the coin and the notebook and guess, without measuring. A ₹5
coin is roughly the width of a thumbnail, and the long side of a notebook is about the length of
your forearm, so a first guess of about 10 coins is reasonable.
Step 2 — Measure both with a 15-cm scale.

WHAT IS MEASURED HOW VALUE

Diameter of the ₹5 coin Place the coin on the scale, read across its widest part 2.5 cm

Long side of the Scale is only 15 cm, so measure 15.0 cm, mark, then 15.0 cm + 9.0 cm = 24.0
notebook measure the rest cm

Step 3 — Calculate.

Number of coins = length of the side ÷ diameter of one coin

= 24.0 cm ÷ 2.5 cm

= 9.6

A coin cannot be cut, so 9 complete coins can be placed.

Length covered by 9 coins = 9 × 2.5 cm = 22.5 cm

Gap left over = 24.0 cm − 22.5 cm = 1.5 cm

Step 4 — Verify. Actually lay 9 coins along the edge, touching one another. You will find they
stop about 1.5 cm short of the corner — exactly as calculated. A tenth coin would need 2.5 cm
and there is only 1.5 cm left, so it will not fit.

Why the answer is 9 and not 10: dividing gives 9.6, and 0.6 of a coin does not exist.
When you are counting whole objects that must fit inside a space, you always take
the whole number below the result.

Page 45 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Try This: Repeat with a ₹1 coin (diameter about 2.0 cm). Now 24.0 ÷ 2.0 = 12 coins
exactly. A smaller coin needs more coins to cover the same length — the same
“smaller unit, bigger number” rule you met with mm and cm.

Q9 Give two examples each for linear, circular and oscillatory motion.

TYPE OF EXAMPLE 1 EXAMPLE 2 WHAT DECIDES IT
MOTION

Linear motion A car moving on a An eraser dropped from The path is a straight line
straight road a height

Circular motion Blades of a running A child on a merry-go- The path is a circle, repeated
ceiling fan round round and round

Oscillatory A child on a swing The pendulum of a wall The path is to and fro about a
motion clock fixed position

More examples you may use instead:

Linear — a lift going up its shaft; a sprinter in the 100 m race; a heavy box being pushed; a
train on a straight track.
Circular — a stone whirled at the end of a thread; the hands of a clock; the wheels of a
moving bicycle; a potter's wheel.
Oscillatory — a see-saw; a plucked metal strip pressed to a table; the needle of a sewing
machine; a branch swaying in the wind.

Remember: circular and oscillatory motion are both periodic — the object repeats
its path after a fixed interval of time. Linear motion is not periodic, because the
object keeps going forward and never returns over the same path.

Page 46 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Q10 Observe different objects around you. It is easier to express the lengths of some
objects in mm, some in cm and some in m. Make a list of three objects in each
category and enter them in the Table 5.6.

SIZE OBJECTS

mm

cm

m

Table 5.6, page 98 — the recording table to be filled in.

Pick the unit that makes the number small and easy to say.

SIZE OBJECTS APPROXIMATE LENGTH

mm Thickness of a coin 2 mm
Thickness of the lead in a pencil 0.7 mm
Length of a grain of rice 7 mm

cm Length of an eraser 4 cm
Length of a chalk stick 8 cm
Width of a mobile phone 7 cm

m Height of a door 2m
Length of the classroom 8m
Height of your teacher 1.6 m

Look at what happens if you use the wrong unit — the length is the same, but the number
becomes clumsy:

Thickness of a coin = 2 mm = 0.2 cm = 0.002 m

Height of a door = 2 m = 200 cm = 2000 mm

The pattern: use mm for things thinner than about a centimetre, cm for things that
fit on your desk, and m for things as big as a room or a person. For anything beyond
a few hundred metres, switch to km.

Page 47 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Try This: Measure the objects you listed and write each length in all three units. You
will see straight away why one of the three is the natural choice.

Q11 A rollercoaster track is made in the shape shown in Fig. 5.19. A ball starts from
point A and escapes through point F. Identify the types of motion of the ball on the
rollercoaster and corresponding portions of the track.

A

D

E
B F

C

Fig. 5.19, page 98 — the rollercoaster track. The ball starts at A and escapes through F.

Follow the ball from A to F and name the shape of the track in each portion.

A
D

E
B F

C
A → B : linear motion B → C → D → E : circular motion E → F : linear
motion

Page 48 of 65

as e
a
Class 6 Science Chapter 5 Measurement of Length and Motion
g l AglaSem · NCERT Solutions

co
Rollercoaster track (as in Fig. 5.19). The straight ramp and the straight exit give linear motion; the
m
e m.
loop gives circular motion.

m l as
m .co a g
l a se
PORTION OF THE TRACK SHAPE OF THAT PORTION TYPE OF MOTION
g
aA to B A straight sloping ramp Linear motion

co m
B to C to D to E
m .
The complete loop — a circular path
e
Circular motion
ag
g l as
a
E to F A straight horizontal run-out Linear motion

So on one ride the ball shows two types of motion — linear on the two straight portions and
co m
se m.
circular on the loop.

o m l a
gthe way round and
m .c loop is circular and not oscillatory: the ball goes all
a
se
Why the

g l a
a
comes out on the far side; it never turns back along the path it came by. In
oscillatory motion the object must return to and fro over the same path.

m a s
em
.co agl
a s
Tip: The ball is fastest at C (the lowest point) and slowest at D (the top of the loop).

a l but the type of motion is decided only by the shape
Speed changes all along thegride,
of the path.

co m
m .
o m l a se
g
.c Tasneem wants to make a metre scale by herself. Sheaconsiders
e m the following

las
Q12

ag
materials for it—plywood, paper, cloth, stretchable rubber and steel. Which of
these should she not use and why?

se m
com g l a
m . a
e

g l
She should not use paper, clothasor stretchable rubber. She can use plywood or steel.
a

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m as e
.co


a g l Page 49 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

MATERIAL USE IT? REASON

Stretchable No — the It stretches when pulled. The marks move apart, so 1 m of rubber can read 1 m
rubber worst choice at one moment and 1.2 m at the next. A scale whose own length changes is
useless.

Cloth No Cloth also stretches a little when pulled, sags when held, frays at the edges, and
shrinks after washing. Its marks will not stay one centimetre apart.

Paper No Paper tears easily, bends and creases, curls with moisture, and cannot be laid
flat and straight against an object. A one-metre paper strip will not stay rigid.

Plywood Yes Stiff, straight and strong; it keeps its length. This is what most classroom metre
scales are made of.

Steel Yes — the Very rigid, does not stretch, tear or bend, and is not affected by damp weather,
best so the markings stay correct for years.

A scale is trustworthy only if

the distance between any two of its marks never changes.

Note the difference from a tailor's tape: a tailor's tape is deliberately made
flexible so that it can go round a curved body — but it is made of coated cloth or
fibreglass that bends without stretching. Flexible is allowed; stretchable is not.

Tip: If Tasneem uses plywood, she should first plane the edge straight and then
mark all 100 centimetres with a good steel scale — because a home-made scale can
never be more accurate than the scale it is copied from.

Q13 Think, design and develop a card game on conversion of units of length to play
with your friends.

Here is a complete game you can make in one period. Design your own version — the marks
are for the idea and the rules, not for copying this one.
Name: Maapak Milan (Match the Measure)
What you need: 40 cards cut from an old greeting card or thick paper, about 7 cm × 5 cm each,
and a sketch pen.

Page 50 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Making the cards — 20 matching pairs. On one card of each pair write a length, and on the
other write the same length in a different unit:

CARD A CARD B (ITS PAIR) CONVERSION USED

1 km 1000 m 1 km = 1000 m

2.5 km 2500 m × 1000

1m 100 cm 1 m = 100 cm

3.5 m 350 cm × 100

1 cm 10 mm 1 cm = 10 mm

7.2 cm 72 mm × 10

1m 1000 mm 100 × 10

0.5 km 500 m × 1000

How to play (2 to 4 players):

1. Shuffle all 40 cards and lay them face down in a 5 × 8 grid.
2. In turn, a player turns over two cards for everyone to see.
3. If the two show the same length in different units, the player must say the conversion
aloud — “2.5 km is 2500 m because 1 km is 1000 m” — and keeps the pair, scoring 1 point
and getting another turn.
4. If they do not match, or the conversion is said wrongly, the cards are turned face down again
and the turn passes.
5. The game ends when all cards are taken. The highest score wins.

Two extra rules to make it harder:

Challenge card: any player may challenge a stated conversion. If the challenge is correct,
the challenger takes the pair instead.
Trap cards: add a few wrong pairs such as “1 km / 100 cm”. Turning up a trap pair costs the
player 1 point — this is exactly the mistake in Question 2(iii).

Why the game teaches well: saying the conversion aloud each time forces you to
use the factor (×1000, ×100, ×10) rather than remembering answers by heart. After
twenty pairs the chain km → m → cm → mm becomes automatic.

Page 51 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Try This: Make a second set with real objects — “thickness of a coin” paired with “2
mm”, “height of a door” with “2 m”. Now the game teaches you to choose the right
unit as well as to convert it.

Learning further — Pages 99 & 100
Extended activities and projects

LEARNING FURTHER

Q1 Can you find the thickness of a single page of your notebook or textbook using a
scale? Think of a way and write it. Carry out the activity and report your result.

Yes — not by measuring one page, but by measuring many pages together and dividing. A
single sheet is about 0.1 mm thick, which is ten times smaller than the smallest division of your
scale, so it cannot be measured directly.
The method:

1. Open the book and note the page numbers of the first and last printed pages of the bunch
you will squeeze — say from page 1 to page 200.
2. Remember that a sheet of paper carries two page numbers, one on each face. So 200 pages
= 100 sheets.
3. Press the bunch flat and tight, without the covers.
4. Measure the thickness of the bunch with a 15-cm scale, holding your eye directly above the
mark.
5. Divide.

Number of pages counted = 200

Number of sheets = 200 ÷ 2 = 100 sheets

Thickness of the bunch (measured) = 1.2 cm = 12 mm

Thickness of one sheet = 12 mm ÷ 100

= 0.12 mm

= 0.12 ÷ 10 cm = 0.012 cm

= 0.12 ÷ 1000 m = 0.00012 m

Page 52 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Result: one page of the notebook is about 0.12 mm thick — about one-eighth of a millimetre.

Why this trick works: the error in reading a scale is about the same (± 0.5 mm)
whether you measure one sheet or a hundred. Spread over 100 sheets, that error
shrinks to ± 0.005 mm per sheet. Measuring many and dividing is a standard way
scientists measure very small quantities.

Tip: The commonest mistake is to divide by the number of pages instead of the
number of sheets, which halves the answer. Count the sheets by feeling the edges if
you are unsure.

Page 53 of 65

as e
Class 6 Science Chapter 5 Measurement of Length and Motion
a g l AglaSem · NCERT Solutions

co m
m.
Collect fallen leaves from the same tree. Identify the name of the tree whose leaves
se
Q2

o m l a
you have taken. Measure length and breadth of all these leaves using a 15-cm scale,
gDiscuss why the
m .c in Fig. 5.20. Record your observations in the Table 5.7.
as shown a
se of the same tree vary in length and breadth.
aleaves
agl

co m
em . ag
g l as 6

a 5
4

com
3
length of the leaf

se m.
2

com l a
1

g
m. a
0 1 2 3 4 5 6 7 8 0

as e breadth of the leaf

g l
15-cm scale (cm marks)

a
a s
. com agl
e m
as across the scale for its breadth.
Fig. 5.20, page 99 — redrawn sketch: the leaf is laid along a 15-cm scale for its length,

a g l
and

. com
a s em OF LEAF
com
S. NO. NAME OF TREE LENGTH OF LEAF BREADTH

. a gl
m
ase
1.

agl
se m
com g l a
m . a
e
as page 99 — the recording table to be filled in.
Tablel5.7,
a g

com
m .
m as e
.co a g l
emalong the midrib from the base of the blade to the tip. For the breadth, turn the scale across the
How to measure a leaf (Fig. 5.20). Place the leaf flat on the table. For the length, lay the scale

a s
agl leaf at its widest part. Read both to the nearest millimetre.
.c
Table 5.7: Length and breadth of leaves — a sample record for the peepal tree:
s e m
m a
em . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 54 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

S. NO. NAME OF TREE LENGTH OF LEAF BREADTH OF LEAF

1. Peepal 11.4 cm 8.2 cm

2. Peepal 9.8 cm 7.0 cm

3. Peepal 12.6 cm 8.9 cm

4. Peepal 10.5 cm 7.6 cm

5. Peepal 8.9 cm 6.4 cm

Longest leaf = 12.6 cm, shortest leaf = 8.9 cm

Difference = 12.6 cm − 8.9 cm = 3.7 cm

So the leaves of one tree can differ by more than 3 cm in length.

Why do leaves of the same tree vary?

Age — a leaf that opened last month is still growing; one that opened last year has reached
full size.
Position on the tree — leaves in bright sunlight at the top are usually smaller and thicker;
leaves in the shade lower down grow broader to catch more light.
Water and nutrients — a branch that gets more water and minerals grows bigger leaves.
Damage — insects, caterpillars, hail and wind tear pieces off, so the measured length or
breadth becomes less.
Natural variation — no two living things are ever exactly identical, just as no two children in
your class are exactly the same height.

The science point: variation is normal in living things. That is why biologists never
rely on one leaf — they measure many and take an average. Notice how different
this is from measuring a pencil, where repeating the measurement gives nearly the
same value every time.

Tip: Collect only fallen leaves, and take all of them from the same tree on the same
day. If you mix two trees, the variation you find will be for a different reason
altogether.

Page 55 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Q3 Discuss with elders in your community what units were used for measurement of
length in the olden days. Also, using the internet, try to find out about the length
scales found in excavations of archaeological sites in India.

Part 1 — Ask your elders. Note down the unit, how it was defined and where it was used. Here
are the units you are most likely to hear about in India:

OLD UNIT HOW IT WAS DEFINED ROUGHLY USED FOR
EQUAL TO

Angula Width of one finger ≈ 1.5–2 cm Carpentry, tailoring, temple
architecture

Balisht Thumb tip to little-finger tip of ≈ 20 cm Cloth, rope, small furniture
(handspan) a spread hand

Haath / hasta Elbow to the tip of the middle ≈ 45 cm Cloth in the bazaar, house
(cubit) finger building

Gaz (yard) Two cubits, roughly nose to ≈ 90 cm Cloth and land measurement
fingertip

Foot / pace Length of a foot; length of one ≈ 25 cm / 75 cm Marking out fields and beds, as
(stride) walking step Padma described

Kos Distance at which a cow's call ≈ 3 km Distances between villages
can be heard

Yojana, dhanusa Ancient units named in Indian Varied by region and Town planning, long journeys
literature period

Part 2 — Scales found in excavations. The Harappan (Indus–Sarasvati) Civilisation, more
than 4000 years old, already had carefully graduated scales:

Lothal (Gujarat) — a small piece of ivory with fine parallel lines, the divisions being about
1.7 mm apart. It is among the finest graduations known from the ancient world.
Mohenjo-daro (present-day Pakistan) — a shell scale with evenly spaced marks about 6.7
mm apart, with a circle-and-dot mark at every fifth division.
Harappa — a broken bronze rod marked in equal lengths.
Kalibangan (Rajasthan) and Dholavira (Gujarat) — the bricks and the street plans follow
fixed ratios, which is only possible if the builders had a common standard of length.

Page 56 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

What this tells us: the Harappan builders used standard units long before the
metre was invented. Their bricks were made in the ratio 1 : 2 : 4 (thickness : width :
length) in city after city, hundreds of kilometres apart — a thing that cannot happen
by accident.

Tip: Write down the elder's exact words and then measure the unit yourself. Ask
your grandmother to show you one haath of cloth, and then measure it with a metre
scale. You will see both how useful and how variable the old units were.

Page 57 of 65

Class 6 Science Chapter 5 Measurement of Length and Motion AglaSem · NCERT Solutions

Q4 Create a maze using lines of 1 cm, 2 cm and their combination. Part of it has been
made for you in Fig. 5.21. Now use your imagination and expand it to a size as big as
you want.

Fig. 5.21, page 100 — the part of the maze already drawn for you, built only from 1 cm
and 2 cm lines.

What to do. Take a squared (graph) sheet in which each small square is 1 cm × 1 cm, or draw
your own 1 cm grid with a 15-cm scale. Then build the walls of the maze along the grid lines,
using only 1 cm and 2 cm strokes.
Steps:

1. Draw a square border, say 10 cm × 10 cm. Leave one 1 cm gap on the left edge for the entry
and one on the right edge for the exit.
2. Inside, draw walls only along grid lines. Each wall must be exactly 1 cm or 2 cm long — use
your scale for every single stroke.
3. First draw one path that runs from entry to exit. Then add dead-end branches on both sides
of it to confuse the player.
4. Use two colours as in Fig. 5.21 — one colour for the 1 cm walls and another for the 2 cm
walls.

Page 58 of 65

as e
a
Class 6 Science Chapter 5 Measurement of Length and Motion
g l AglaSem · NCERT Solutions

5. Trade mazes with a friend and time each other solving them.
co m
e m.
m l as
m .co
A 10 cm × 10 cm maze on a 1 cm grid
a g
l a se
g
= 10 × 10 = 100 unit squares
aNumber of grid lines available for walls = 11 across + 11 down

com
. ag
Total wall length if you drew every line = 11 × 10 cm × 2 = 220 cm = 2.2 m
e m
g l as
a
Where the measuring comes in: the maze is a drawing exercise and a measuring
exercise. Every stroke must be checked against the scale, so by the time the maze is
co m
finished you will have used the 15-cm scale a hundred times and 1 cm will have
em.
m l as
.co g
become a length you can judge by eye.
m a
l a se
a g Try This: Make the same maze again with all lengths doubled — 2 cm and 4 cm
walls on a 20 cm × 20 cm sheet. The shape stays the same but every length is twice
m a s
.co
as large. This idea of scaling up is used by every map maker.
m agl
l a se
a g

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 59 of 65