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๐ฌ Think about it
To find density you need two things: mass and volume. Mass is easy with a balance. But how do you find the volume of an odd-shaped stone? You can't use a ruler! There's a clever water trick. Let's learn to measure both.
How do we measure the mass of an object?
- Mass is the quantity of matter in an object.
- It is measured using a balance.
- A digital weighing balance shows mass directly.
- First set it to zero (tare), then place the object.
Example:
A stone placed on a tared digital balance may read 16.400 g.
In this Activity, we will measure the mass of a solid using a digital weighing balance.
Materials needed
A digital weighing balance, a dry clean watch glass or butter paper, a stone or solid object.
Procedure
1. Switch on the digital weighing balance.
2. Observe the initial reading; it should show zero.
3. If not zero, press the tare or reset button.
4. Place a dry, clean watch glass on the pan and note the reading.
5. Reset the balance to zero by pressing the tare button.
6. Carefully place the solid object on the watch glass.
7. Note the reading, which gives the mass of the object (say 16.400 g).
2. Observe the initial reading; it should show zero.
3. If not zero, press the tare or reset button.
4. Place a dry, clean watch glass on the pan and note the reading.
5. Reset the balance to zero by pressing the tare button.
6. Carefully place the solid object on the watch glass.
7. Note the reading, which gives the mass of the object (say 16.400 g).
Observation
The balance shows the mass of the object once it is placed on the tared watch glass.
Explanation
Taring removes the mass of the watch glass, so the balance shows only the object's mass. (For a liquid, replace the watch glass with a beaker.)
โ Summary
- Balance switched on
- Tared to zero
- Object placed
- Mass read off
๐ก Note
- The mass of a liquid is measured by replacing the watch glass with a beaker.
- Pour the desired amount of liquid into the beaker and read the mass.
How is mass different from weight?
- Mass is the quantity of matter; its units are g and kg.
- Weight is the force of Earth's pull, measured in newtons.
- Most balances really measure weight.
- But their scales are marked in mass units like grams.
Mass
Weight
Quantity of matter in an object.
Force with which Earth attracts it.
Measured in gram (g) and kilogram (kg).
Measured in newtons (N).
โก A step further
- The words "mass" and "weight" are often used interchangeably in everyday language.
- In science they mean different things.
- Mass is the quantity of matter in an object; units gram (g) and kilogram (kg).
- Weight is the force with which Earth attracts an object; measured in newtons (N).
- Most balances actually measure weight but show values in mass units (g or kg).
- Two-pan balances are the exception (they compare masses directly).
How do we measure the volume of liquids?
- Volume is the space occupied by an object.
- Liquids are measured with a measuring cylinder.
- It is a tall narrow tube with volume markings.
- Its smallest reading depends on its capacity.
Example:
A 100 mL measuring cylinder can read down to 1 mL, so it is best for measuring 70 mL.
In this Activity, we will find the smallest volume a measuring cylinder can read.
Materials needed
A measuring cylinder (say 100 mL).
Procedure
1. Take a measuring cylinder and observe it carefully.
2. Note the maximum volume it can measure (its capacity).
3. Find the volume difference between two bigger marks, e.g. 10 mL and 20 mL.
4. Count the small divisions between those two marks.
5. Work out the volume of one small division.
2. Note the maximum volume it can measure (its capacity).
3. Find the volume difference between two bigger marks, e.g. 10 mL and 20 mL.
4. Count the small divisions between those two marks.
5. Work out the volume of one small division.
Observation
For the 100 mL cylinder, the gap between 10 mL and 20 mL is 10 mL with 10 divisions, so one division reads 10 ÷ 10 = 1 mL.
Explanation
The smallest volume a cylinder can read depends on its capacity. A 100 mL cylinder reads 1 mL, so it can measure 70 mL accurately in one step — the best choice for that amount.
โ Summary
- Cylinder observed
- Marks and divisions counted
- One division found
- Smallest reading known
In this Activity, we will measure 50 mL of water correctly by reading the meniscus.
Materials needed
A clean dry measuring cylinder, water, a dropper, a container.
Procedure
1. Place a clean, dry measuring cylinder on a flat surface.
2. Pour water slowly into it up to the required mark.
3. Adjust the level with a dropper by adding or removing water.
4. Notice the curved water surface, called the meniscus.
5. Read the mark at the bottom of the meniscus for colourless liquids.
6. Keep your eyes level with the bottom of the meniscus.
7. At 50 mL, transfer the water to the required container.
2. Pour water slowly into it up to the required mark.
3. Adjust the level with a dropper by adding or removing water.
4. Notice the curved water surface, called the meniscus.
5. Read the mark at the bottom of the meniscus for colourless liquids.
6. Keep your eyes level with the bottom of the meniscus.
7. At 50 mL, transfer the water to the required container.
Observation
The water forms a curved meniscus; the correct reading is taken at the bottom of the curve, with the eye at the same level.
Explanation
Reading at the bottom of the meniscus with the eye at level avoids error. For coloured liquids, the mark should coincide with the top of the meniscus.
โ Summary
- Water poured in
- Level adjusted
- Meniscus formed
- Read at eye level
In this Activity, we will calculate the volume of a regular cuboid object using its measurements.
Materials needed
Cuboid objects (a notebook, a shoe box, or a dice), a scale.
Procedure
1. Collect objects with a cuboid shape.
2. Measure the length (l), width (w), and height (h) with a scale.
3. Suppose length 25 cm, width 18 cm, height 2 cm.
4. Calculate the volume using Volume = l × w × h.
5. Record the result in your notebook.
2. Measure the length (l), width (w), and height (h) with a scale.
3. Suppose length 25 cm, width 18 cm, height 2 cm.
4. Calculate the volume using Volume = l × w × h.
5. Record the result in your notebook.
Observation
Volume = 25 cm × 18 cm × 2 cm = 900 cm³.
Explanation
For a regular shape, the volume is found by multiplying its length, width, and height — no water needed.
โ Summary
- Cuboid measured
- l, w, h noted
- Multiplied together
- Volume found
How do we find the volume of an irregular object like a stone?
- A stone has no regular shape, so a scale won't work.
- Lower it into water in a measuring cylinder.
- The water level rises by the object's volume.
- Volume of object = final volume − initial volume.
In this Activity, we will find the volume of an irregular solid by water displacement.
Materials needed
A measuring cylinder, water, a stone or metal key, thread.
Procedure
1. Collect objects such as a stone or metal keys.
2. Fill a measuring cylinder with water to a desired volume, say 50 mL, and record it.
3. Tie the object with a thread and slowly lower it into the cylinder.
4. Record the final volume after the level rises, say 55 mL.
5. Subtract the initial volume from the final volume to get the object's volume.
6. Record all observations in Table 9.2.
2. Fill a measuring cylinder with water to a desired volume, say 50 mL, and record it.
3. Tie the object with a thread and slowly lower it into the cylinder.
4. Record the final volume after the level rises, say 55 mL.
5. Subtract the initial volume from the final volume to get the object's volume.
6. Record all observations in Table 9.2.
Table 9.2 — Volume of irregular solids
| S.No. | Object | Initial volume of water in the measuring cylinder (mL) (A) | Final volume of water in the measuring cylinder (mL) (B) | Volume of water displaced in the measuring cylinder (mL) (B–A) | Volume of the object (cm³) |
|---|---|---|---|---|---|
| 1. | Stone | 50 mL | 55 mL | 5 mL | 5 cm³ |
| 2. | Metal key | 50 mL | 53 mL | 3 mL | 3 cm³ |
| 3. | Any other | 50 mL | 58 mL | 8 mL | 8 cm³ |
Observation
The water level rises when the object is lowered in. For the stone, 55 mL − 50 mL = 5 mL, so its volume is 5 cm³.
Explanation
The object pushes aside (displaces) its own volume of water, so the rise in level equals the object's volume. Volume in mL equals the same number in cm³ for solids.
โ Summary
- Water level noted
- Object lowered in
- Level rises
- Difference = volume
๐ก Note
- The values of volume are obtained in millilitres (mL).
- For solids, mL can be written in the equivalent unit cm³.
How do we calculate the density of the stone?
- We now have the mass and the volume.
- Mass of the stone is 16.400 g; volume is 5 cm³.
- Density = mass ÷ volume.
- So the density is 3.28 g/cm³.
Density
=
\( \dfrac{\text{Mass}}{\text{Volume}} = \dfrac{16.400\ \text{g}}{5\ \text{cm}^3} = 3.28\ \text{g/cm}^3 \)
๐ก Ever heard of ...
- Before big ships, people used bamboo and wooden logs to travel water.
- Bamboo is light, hollow, and floats easily.
- Bamboo poles were tied into rafts and small boats.
- Such traditional boats are still used in some regions today.
๐ก Let us dig deeper!
- Earth has layers: crust, upper mantle, lower mantle, outer and inner core.
- The crust is the lightest, outermost layer.
- Density increases as we move toward the centre.
- Deeper down, higher pressure and heat make materials more compact.
Important Points
- Mass is found with a balance; regular volume with l × w × h.
- Irregular volume is found by water displacement.
- Density = mass ÷ volume, as for the stone (3.28 g/cm³).
โ Test Yourself
-
What instrument measures mass?
View Answer
A balance, such as a digital weighing balance, measures mass in grams or kilograms. -
Why tare a balance before weighing?
View Answer
Taring sets it to zero so the watch glass's mass is removed and only the object's mass is shown. -
What is the meniscus?
View Answer
The curved surface of water in a measuring cylinder. Read colourless liquids at the bottom of the meniscus. -
How do you find the volume of a stone?
View Answer
Lower it into water in a measuring cylinder; the rise in water level equals the stone's volume. -
If mass is 16.4 g and volume 5 cm³, what is the density?
View Answer
Density = 16.4 ÷ 5 = 3.28 g/cm³.
Important Definitions
- Mass — the quantity of matter present in an object, measured in g or kg.
- Weight — the force with which Earth attracts an object, measured in newtons.
- Volume — the space occupied by an object or substance.
- Measuring cylinder — a tall narrow apparatus with markings used to measure the volume of liquids.
- Meniscus — the curved surface that a liquid forms in a measuring cylinder.
๐ NCERT Question 10 — Reema has a piece
Reema reshapes 120 g of clay from a cube into a sheet. Predict what happens to its density.
View Answer →
