NCERT Solutions Curiosity Chapter 5 Chapter exercises — Let us enhance our learning

Book page 97 & 98 Updated on2026-09-05

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.

Answer

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

Column I	Matches with (Column II)	Typical value	Why this unit
Distance between Delhi and Lucknow	kilometre	≈ 500 km	In metres it would be 5,00,000 m — far too long a number
Thickness of a coin	millimetre	≈ 2 mm	In centimetres it is only 0.2 cm; mm gives a whole number
Length of an eraser	centimetre	≈ 4 cm	Fits neatly on a 15-cm scale
Length of school ground	metre	≈ 100 m	In km it would be 0.1 km — an awkward decimal

Check with the conversion factors:
500 km = 500 × 1000 m = 5,00,000 m (1 km = 1000 m)
2 mm = 2 × 0.1 cm = 0.2 cm (1 mm = 0.1 cm)
100 m = 100 ÷ 1000 km = 0.1 km

The rule of thumb: choose the unit for which the number comes out roughly between 1 and 1000. That is why we say 500 km, not 5,00,000 m — and 2 mm, not 0.002 m.

Q2.

Read the following statements and mark True (T) or False (F) against each. (i) The motion of a car moving on a straight road is an example of linear motion. (ii) Any object which is changing its position with respect to a reference point with time is said to be in motion. (iii) 1 km = 100 cm

Answer

	Statement	T / F
(i)	The motion of a car moving on a straight road is an example of linear motion.	True (T)
(ii)	Any object which is changing its position with respect to a reference point with time is said to be in motion.	True (T)
(iii)	1 km = 100 cm	False (F)

(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

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) centimetre	Standard	1 m = 100 cm, the same for everyone
(iii) kilometre	Standard	1 km = 1000 m, the same for everyone
(iv) handspan	Not standard	Its size depends on whose hand it is — Deepa, Anish and Hardeep all got different numbers for the same table

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.

Answer

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 device	Total length it can measure	Smallest value it can measure
15-cm plastic scale (geometry box)	15 cm	1 mm = 0.1 cm
30-cm plastic scale	30 cm	1 mm
Wooden metre scale (blackboard)	100 cm = 1 m	1 mm
Tailor's cloth measuring tape	150 cm	1 mm (some show only 0.5 cm)
Steel measuring tape (carpenter)	3 m or 5 m	1 mm
Long tape for the playground	30 m	1 cm
Tape printed only in centimetres	150 cm	1 cm

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.

Answer

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

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.

Answer

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

Steps:

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

Why the thread must not stretch: a stretched thread needs more length to go round, so the reading comes out too large. Cotton or jute thread is ideal; a rubber band is the worst possible choice.

Tip: Wrap the thread only once round. If it accidentally goes round twice, you will get about 44 cm and must halve it.

Q7.

Measure the height of your friend and express it in (i) metres (ii) centimetres and (iii) millimetres.

Answer

Method. Ask your friend to stand straight against a wall, without shoes, heels touching the wall and looking straight ahead. Place a book flat on the head, touching the wall, and mark the wall along the lower edge of the book. Measure from the floor to the mark with a metre scale or a measuring tape.

Suppose the mark is at 142 cm. Then:

Asked in	Conversion factor used	Working	Answer
(ii) centimetres	measured directly	—	142 cm
(i) metres	1 m = 100 cm	142 ÷ 100	1.42 m
(iii) millimetres	1 cm = 10 mm	142 × 10	1420 mm

Height = 142 cm
In metres: 142 cm ÷ 100 = 1.42 m
In millimetres: 142 cm × 10 = 1420 mm
Check: 1.42 m × 1000 mm/m = 1420 mm ✓

Measure your friend and put your own number in. Most Class 6 students are between 1.30 m and 1.55 m tall.

Note the direction of each conversion: cm → m goes to a bigger unit, so we divide and the number gets smaller (142 → 1.42). cm → mm goes to a smaller unit, so we multiply and the number gets bigger (142 → 1420). The height itself never changed.

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.

Answer

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

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.

Answer

Type of motion	Example 1	Example 2	What decides it
Linear motion	A car moving on a straight road	An eraser dropped from a height	The path is a straight line
Circular motion	Blades of a running ceiling fan	A child on a merry-go-round	The path is a circle, repeated round and round
Oscillatory motion	A child on a swing	The pendulum of a wall clock	The path is to and fro about a 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.

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.

Answer

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

Size	Objects	Approximate length
mm	Thickness of a coin Thickness of the lead in a pencil Length of a grain of rice	2 mm 0.7 mm 7 mm
cm	Length of an eraser Length of a chalk stick Width of a mobile phone	4 cm 8 cm 7 cm
m	Height of a door Length of the classroom Height of your teacher	2 m 8 m 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.

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.

Answer

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

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

Portion of the track	Shape of that portion	Type of motion
A to B	A straight sloping ramp	Linear motion
B to C to D to E	The complete loop — a circular path	Circular motion
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 circular on the loop.

Why the loop is circular and not oscillatory: the ball goes all the way round and 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.

Tip: The ball is fastest at C (the lowest point) and slowest at D (the top of the loop). Speed changes all along the ride, but the type of motion is decided only by the shape of the path.

Q12.

Tasneem wants to make a metre scale by herself. She considers the following materials for it—plywood, paper, cloth, stretchable rubber and steel. Which of these should she not use and why?

Answer

She should not use paper, cloth or stretchable rubber. She can use plywood or steel.

Material	Use it?	Reason
Stretchable rubber	No — the worst choice	It stretches when pulled. The marks move apart, so 1 m of rubber can read 1 m 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 best	Very rigid, does not stretch, tear or bend, and is not affected by damp weather, 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.

Answer

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.

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
1 m	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
1 m	1000 mm	100 × 10
0.5 km	500 m	× 1000

How to play (2 to 4 players):

Shuffle all 40 cards and lay them face down in a 5 × 8 grid.
In turn, a player turns over two cards for everyone to see.
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.
If they do not match, or the conversion is said wrongly, the cards are turned face down again and the turn passes.
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.

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.

Was this helpful? Report an error