NCERT Solutions Curiosity Chapter 5 Extended activities and projects — Learning further

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.

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

How to measure a leaf (Fig. 5.20). Place the leaf flat on the table. For the length, lay the scale along the midrib from the base of the blade to the tip. For the breadth, turn the scale across the leaf at its widest part. Read both to the nearest millimetre.

Table 5.7: Length and breadth of leaves — a sample record for the peepal tree:

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.

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:

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.

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.
5. Trade mazes with a friend and time each other solving them.

Method — do it exactly the same way every time, or the comparison is meaningless.

1. Choose a wall with a flat, hard floor in front of it — never a carpet.
2. Stand with your heels, back and head touching the wall, feet together, without shoes, looking straight ahead.
3. An adult places a book or a set square flat on your head, pressed against the wall, and draws a fine pencil mark along its lower edge.
4. Measure from the floor to the mark with a measuring tape or metre scale, keeping the tape vertical and the eye level with the mark.
5. Write the date and the height in a table. Repeat every three months.

Sample height record — keep one like this in your notebook:

The idea: the strip strikes the frame once in every complete turn of the wheel. So the number of sounds is the number of turns, and each turn carries the bicycle forward by exactly one wheel-boundary length (the circumference).

Step 1 — Measure the boundary of the wheel using a string, exactly as in Fig. 5.8. Wrap the string once round the tyre, mark it, straighten it and measure it on a metre scale.

Step 2 — Ride slowly and count the sounds. Suppose you count 500 sounds between the school gate and the market.

Step 3 — Check with a second method. Walk the same stretch counting your steps. If your step is 0.6 m and you take 1750 steps, the distance is 0.6 × 1750 = 1050 m — the two answers agree.

What is a Jones Counter? It is a small mechanical counter clamped to the front axle of a bicycle, geared to the wheel. Instead of making a sound, it silently counts a fixed number of clicks per revolution — around 23 per turn — so it can measure a fraction of a turn. It is the instrument officially used to certify the length of road-running courses such as marathons. Before a race the bicycle is first ridden over a carefully measured stretch (a calibration course) to find how many counts equal one kilometre, and then over the race route.