ICSE Class 8 Physics Chapter 02 Physical Quantities

Physical Quantities And Measurement

Theme

Previous learning demonstrated the measurement of the density of regular solids. In this class children will develop the ability to measure the density of an irregular solid and also of a given liquid. They will also understand that due to the difference in the value of densities of a solid and liquid, a piece of solid can float or sink in a liquid.

In This Chapter You Will Learn To

Measure density of an irregular solid

Measure density of a liquid

Discuss the concept of floatation based on relative densities of solid and liquid

Express result of measurement in proper unit with proper symbol

Solve simple numerical problems based on formula of density

Compare densities of matter in three states, solid, liquid and gas

Make careful observations including measurements

Gather data using formal units

Make conclusions from collected data

Make predictions using scientific knowledge and effectively communicating the same.

Learning Objectives

Revising previous concepts learnt by children.

Building on children's previous learning.

Demonstrating the process of measurement of density of an irregular solid.

Demonstrating The Process Of Measurement

Demonstrating the process of measurement of density of a liquid.

Engaging children in practical tasks involving measurement of density of an irregular solid and a liquid.

Engaging children (in group/pairs/individually) in an investigation to find out which object floats in which liquid, given solids of different densities and liquids of different densities. This is to be followed by discussion.

Guiding children to predict the result of the previous investigation and compare predictions with the outcomes.

Knowing Concepts

Measurement of density of irregular solids using: Eureka can, Measuring cylinder

Measurement of density of fluids: Basic concept, Concept of floatation and sinking of a substance (relate to density)

Comparison of densities in the three states of matter.

Density

Each body has a certain mass and a definite volume. The volume occupied by a body increases, if its mass is increased. Similarly, the mass of a body increases on increasing its volume. Further, it is found that

1. Equal masses of different substances have different volumes. For example, the volume of cotton is much larger than the volume of an equal mass of lead. This is because the particles of lead are closely packed while those of cotton are very loosely packed. In other words, lead is denser than cotton.

2. Equal volumes of different substances have different masses. For example, the mass of iron is much more than the mass of an equal volume of wood. This is because the particles of iron are more closely packed than those of the wood. In other words, iron is denser than wood. Thus, to explain that equal volumes of different substances have different masses or equal masses of different substances have different volumes, we use a term called density. It is defined as follows:

The density of a substance is its mass per unit volume i.e.

Density of a substance = \[\frac{\text{Mass of the substance}}{\text{Volume of the substance}}\]

The density of a substance is represented by the symbol d. If mass of a substance is M and its volume is V, its density will be

\[d = \frac{M}{V}\]

Unit Of Density

Unit of density = \[\frac{\text{Unit of mass}}{\text{Unit of volume}}\]

In S.I. system, unit of mass is kg and unit of volume is m³, so S.I. unit of density is \[\text{kg m}^{-3}\] (kilogram per cubic metre). In C.G.S. system unit of mass is g and unit of volume is cm³, so CGS unit of density is g cm⁻³ (gram per cubic centimetre).

Relationship Between S.I. And C.G.S. Units

\[1 \text{ kg m}^{-3} = \frac{1\text{ kg}}{1\text{ m}^3} = \frac{1000\text{ g}}{(100\text{ cm})^3} = \frac{1}{1000} \text{ g cm}^{-3}\]

Thus,

\[1 \text{ kg m}^{-3} = 10^{-3} \text{ g cm}^{-3}\]

or \[1 \text{ g cm}^{-3} = 1000 \text{ kg m}^{-3}\]

Examples

1. The mass of an iron cube of volume 10 cm³ is found to be equal to 78 g.

Therefore, density of iron = \[\frac{78 \text{ g}}{10\text{ cm}^3} = 7.8 \text{ g cm}^{-3}\]

2. The mass of 1 cm³ of water is 1 g, hence, density of water = \[\frac{1\text{ g}}{1\text{ cm}^3} = 1 \text{ g cm}^{-3}\]

3. A piece of copper of mass 8.9 kg has volume 0.001 m³. The density of copper is \[\frac{8.9 \text{ kg}}{0.001 \text{ m}^3} = 8900 \text{ kg m}^{-3}\]

Do You Know?

1. The density of a substance does not change with any change in its shape or size.

2. Almost all substances expand on heating and contract on cooling, but their mass does not change. So the density of a substance decreases with the increase in temperature and increases with the decrease in temperature. Exception is water which contracts on heating from 0°C to 4°C and expands on heating above 4°C. So the density of water increases from 0°C to 4°C and then decreases above 4°C (i.e. the density of water is maximum at 4°C which is equal to 1000 kg m⁻³).

Determination Of Density Of A Regular Solid

1. First measure the mass M of the given regular solid by using a beam balance.

2. Now to find the volume V of the given regular solid, use the following formula:

Volume of cube = (one side)³

Volume of cuboid = length × breadth × height

Volume of sphere = \[\frac{4}{3} \pi \text{ (radius)}^3\]

Volume of cylinder = \[\pi \text{ (radius)}^2 \times \text{height}\]

(where \[\pi = 3.14\])

The side of cube or length, breadth and height of cuboid or radius of sphere or radius and height of cylinder can be measured with the use of a metre ruler.

3. Knowing mass M and volume V, calculate density d of the substance of the given regular body by using the formula

\[d = \frac{M}{V}\]

For example, if mass of a cube of iron is M = 210 g

One side of cube = 3 cm

Volume of cube V = (one side)³ = (3)³ = 27 cm³

Density of iron d = \[\frac{M}{V} = \frac{210 \text{ g}}{27 \text{ cm}^3} = 7.78 \text{ g cm}^{-3}\]

Teacher's Note

When students calculate the density of objects like their textbook or a piece of chalk, they understand that denser objects feel heavier for the same size, like how a metal block feels much heavier than a wooden block of the same dimensions.

Vessels For Measuring Volume

In class VII, you have read that we use different vessels for measuring the volume of liquids. Some of the vessels are given below.

Measuring Cylinder

It is made up of glass or plastic and is graduated in millilitre (mL) with its zero mark at the bottom. The graduation line increase upwards as shown in Fig. 2.1. We have measuring cylinders available of different capacities, such as 50 mL, 100 mL, 200 mL, 500 mL etc. The capacity of measuring cylinder is marked on it.

Measuring Beaker

A measuring beaker is made up of glass, plastic or metal like aluminium. It is used to take out a fixed volume of liquids (say milk, oil etc.) such as 50 mL, 100 mL, 200 mL, 500 mL, 1 litre from a large container. The capacity of measuring beaker is marked on it.

Eureka Can

A Eureka can is a glass (or polythene or metal) beaker with a side opening near its mouth which is known as spout. Thus, the beaker can contain a volume of liquid up to the spout. Any excess liquid overflows through the spout. It is shown in Fig. 2.3.

Teacher's Note

When students use measuring cylinders in the kitchen to measure liquids for cooking or baking recipes, they see how precise measurements ensure consistent results, just like how density measurements ensure accuracy in scientific experiments.

Determination Of Density Of An Irregular Solid

To determine the density of an irregular solid, we have to measure its mass and volume. The mass of the body is measured with the help of beam balance. To measure the volume of the solid, we use the displacement method i.e. a solid when immersed in a liquid, displaces volume of liquid equal to its own volume. The measurement of volume of an irregular body by displacement can be understood by the following activities.

Activity 1

1. Measure the mass of the given solid using a common beam balance. Note the mass. Let it be M gram.

2. Take a measuring cylinder. Fill it partly with water as shown in Fig. 2.4 (a)

3. Note the level of water. Let it be V₁ mL.

4. Now tie the given solid with a thread and gently lower the solid in water contained in measuring cylinder as shown in Fig. 2.4 (b). Take care that no water splashes out. Note the level of water again. Let it be V₂ mL.

5. Find the difference, V₂ - V₁. It gives the volume V of the solid i.e.

V = (V₂ - V₁) cm³

6. Then, calculate the density of the solid by using the following formula:

Density = \[\frac{\text{Mass}}{\text{Volume}} = \frac{M}{V} \text{ g cm}^{-3}\]

If M = 78 g, V = 10 cm³, then

Density = \[\frac{78 \text{ g}}{10\text{ cm}^3} = 7.8 \text{ g cm}^{-3}\]

Note : 1 mL = 1 cm³.

Activity 2

1. Take an Eureka can. Place the Eureka can on the table with a measuring cylinder under its spout as shown in Fig. 2.5 (a). Pour water into the can until it starts overflowing through the spout. When the water has stopped dripping, remove the measuring cylinder. Empty it, dry it and again place it under the spout.

2. Now tie the given irregular solid by a thread. Immerse the solid gently into the water contained in the Eureka can as shown in Fig. 2.5(b). The solid displaces water equal to its own volume which overflows through the spout and gets collected in the measuring cylinder. When water stops dripping out through the spout, note the volume of water collected in the measuring cylinder.

3. Dry the solid. Measure the mass M of the given solid with a beam balance.

Let mass of solid M = 310 g

Volume of solid V = volume of water collected in the measuring cylinder = 40 cm³

Density d = \[\frac{\text{Mass M}}{\text{Volume V}} = \frac{310 \text{ g}}{40 \text{ cm}^3} = 7.75 \text{ g cm}^{-3}\]

Teacher's Note

When children bathe or wash dishes, they observe water displacement and realize how volume changes when objects are placed in water - this same principle helps scientists measure the exact volume of irregularly shaped objects like stones or metal pieces.

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