Measuring with body parts and the need for units
Two friends measure the same desk with their handspans and get 8 and 6. Both are right, yet they disagree.
Length is the distance between two points. People once used the handspan, cubit (forearm) and pace, but these change from person to person. So we need a standard unit that is the same for everyone.
In the figure: A smaller hand gives a larger count, so spans cannot be compared.
Rule 1: Body-part units — Handy but not exact.
- Easy: Handspan, cubit, footstep and pace were used.
- Medium: A bigger person gets a smaller count for the same length.
- Exam-type: Counts also change if the same person measures again.
Rule 2: Why a standard unit — Everyone must get the same answer.
- Easy: A fixed unit lets us compare and trade fairly.
- Medium: Tailors, builders and shopkeepers all need it.
- Exam-type: The metre was agreed as the standard unit of length.
Always write the unit with the number; "5" alone means nothing.
Thinking handspans from two people can be added or compared.
"Body parts vary; standard units agree."
Practice questions
- 1Which unit is most likely to give different results for different people?
- 2Hardeep counted 14 handspans and Padma 13 for the same table. Whose handspan is likely smaller?
- 3Hardeep's grandmother measures cloth using —
- 4A farmer divides his field into beds by —
- 5Why did the number of handspans for the same table differ among the friends?
- 6Char angula means —
- 7Which of these is a unit based on a body part?
- 8Deepa's mother calls the handspan —
Show answers (try them yourself first)
- 1A handspan
- 2Hardeep's
- 3the length of her arm
- 4walking and counting his strides
- 5Their handspans are of different sizes
- 6four fingers' width
- 7Handspan
- 8balisht
Standard units of length
Cloth is sold in metres, a pencil is measured in centimetres, and the distance between two cities is given in kilometres.
The metre (m) is the SI unit of length. Small lengths use the centimetre (cm) and millimetre (mm); long distances use the kilometre (km). Choose the unit that suits the size of what you measure.
Formula: 1 m = 100 cm, 1 cm = 10 mm, 1 km = 1000 m
In the figure: A pencil of 6.3 cm: the tip lies between 6 and 7, closer to 6.
Rule 1: Changing units — Multiply to go to a smaller unit, divide to go to a larger one.
- Easy: 2 m = 2 × 100 = 200 cm.
- Medium: 350 cm = 350 ÷ 100 = 3.5 m.
- Exam-type: 4 cm = 4 × 10 = 40 mm.
Rule 2: Choosing a unit — Pick the unit that gives a handy number.
- Easy: Thickness of a coin: mm.
- Medium: Length of a classroom: m.
- Exam-type: Distance between two towns: km.
Convert to the same unit before you add or compare lengths.
Writing 1 m = 10 cm instead of 100 cm.
"Metre hundred, centimetre ten, kilometre thousand."
Practice questions
- 1Which unit suits the distance between Delhi and Lucknow?
- 2Which unit suits the thickness of a coin?
- 3Which unit suits the length of an eraser?
- 4Which unit suits the length of a school ground?
- 5SI stands for —
- 6The SI unit of length is —
- 7A centimetre is divided into 10 equal parts. Each part is a —
- 81 cm is equal to —
Show answers (try them yourself first)
- 1Kilometre
- 2Millimetre
- 3Centimetre
- 4Metre
- 5International System of Units
- 6metre
- 7millimetre
- 810 mm
Correct way of measuring length
A tailor places the tape flat along the cloth, starts at its zero end and reads straight from above.
Place the scale along the object with its zero at one end and the edge touching it. Keep your eye directly above the mark. Reading from a side gives a parallax error. If the end of the scale is worn, start from the 1 cm mark and subtract 1 cm. A curved line is measured with a thread.
In the figure: Only the eye straight above the mark reads the true value.
Rule 1: Placing and reading — Three checks: zero, edge, eye.
- Easy: Match zero with one end of the object.
- Medium: Keep the scale close and flat against the object.
- Exam-type: Read the mark nearest to the other end.
Rule 2: Curved lengths and worn scales — Use a trick when the plain method fails.
- Easy: Lay a thread along a curve, straighten it, then measure it.
- Medium: Worn zero end: start at 1 cm and subtract 1 cm.
- Exam-type: Measure a long length in parts and add them.
Take the reading two or three times; the same answer builds confidence.
Reading from the side and keeping the scale away from the object.
"Zero, edge, eye."
Practice questions
- 1Which is more suitable to measure the girth of a tree?
- 2Which scale is best for measuring the width of your notebook?
- 3To measure the length of a pencil, you may use —
- 4While reading the scale, the eye should be —
- 5Using a broken scale, an object starts at the 2.0 cm mark and ends at 8.5 cm. Its length is —
- 6A measurement result consists of —
- 7The height of a room can be measured using —
- 8The scale should be placed —
Show answers (try them yourself first)
- 1A flexible measuring tape
- 2A 15-cm scale
- 3a 15-cm scale
- 4directly above the point being read
- 56.5 cm
- 6a number and a unit
- 7a metre scale or measuring tape
- 8in contact with the object along its length
Reference point, rest and motion
A passenger sits still in a moving bus, yet a person standing on the road sees her going by.
An object is in motion if its position changes with time with respect to a reference point; if it does not change, it is at rest. Rest and motion depend on the reference point: the passenger is at rest with respect to the bus but moving with respect to the road.
In the figure: The car moves with respect to the tree because their distance changes.
Rule 1: Reference point — Name the thing you compare with.
- Easy: A tree, a pole or a building can be a reference point.
- Medium: Position is described from the reference point.
- Exam-type: Change the reference point and the answer may change.
Rule 2: Rest and motion — Always say "with respect to what".
- Easy: A seated passenger is at rest with respect to the bus.
- Medium: The same passenger moves with respect to the road.
- Exam-type: Trees seem to move backwards to a person in a train.
Before saying moving or at rest, first state the reference point.
Saying something is absolutely at rest without any reference point.
"Compare, then say: moving or rest."
Practice questions
- 1A fixed object or point from which distances are stated is called —
- 2Why did the friends' observations about the school and garden differ?
- 3The kilometre stone reads 'Delhi 70 km'. Padma's position is —
- 4An object is at rest if —
- 5Kilometre stones on the roadside indicate —
- 6If all friends measured distances of school and garden from the same bus stand, their observations would —
- 7For drawing the Kabaddi court, the students first —
- 8In the kilometre stone example, the reference point is —
Show answers (try them yourself first)
- 1a reference point
- 2Each located the distances from their own house
- 370 km from Delhi
- 4its position does not change with respect to a reference point with time
- 5the distance from a place
- 6be the same
- 7decided a point on the ground from which to measure
- 8Delhi
Reference point, rest and motion
In the app you can move this figure with your finger.
Open in the appTypes of motion
A ball rolls straight, a fan blade turns around, a swing goes to and fro, and a bee flies in all directions.
Linear motion is along a straight line. Circular motion is along a circle. Oscillatory motion is to and fro about a fixed point. Random motion has no fixed path or pattern. A motion that repeats after equal time intervals is periodic.
In the figure: Four kinds of motion: straight, circular, to-and-fro and random.
Rule 1: Linear and circular — Look at the path.
- Easy: A car on a straight road: linear.
- Medium: A merry-go-round or fan blade: circular.
- Exam-type: Both can repeat, so they can be periodic.
Rule 2: Oscillatory and random — To and fro about a middle point, or no pattern at all.
- Easy: A swing or a pendulum: oscillatory.
- Medium: Children in a playground: random.
- Exam-type: A guitar string vibrates to and fro too.
Describe the path first, then name the type of motion.
Calling every repeating motion circular.
"Line, circle, to-and-fro, no pattern."
Practice questions
- 1A student says all motion is linear. Which example shows she is wrong?
- 2Which motion repeats along a circular path again and again?
- 3Motion along a straight line is called —
- 4Motion along a circular path is called —
- 5A car moving on a straight road shows —
- 6An eraser hung from a thread, taken slightly aside and released, shows —
- 7Circular and oscillatory motions are both —
- 8Motion to and fro about a fixed position is called —
Show answers (try them yourself first)
- 1A merry-go-round
- 2Circular motion
- 3linear motion
- 4circular motion
- 5linear motion
- 6oscillatory motion
- 7periodic
- 8oscillatory motion