CBSE Class 7 Science Advanced Physics Measurements Notes Set 01

Measurements

Introduction

The word 'science' means to know. It is derived from the Latin word 'scire'. Science attempts to know the unknown, and during this process great discoveries are made. Physical sciences deal with the study of inanimate objects in nature. Physics and chemistry are its main branches.

Physics deals with the properties of matter. For example, it talks about how dense and elastic a matter is. It deals with the external behaviour of matter. For example, how matter behaves when a force is applied on it. It also deals with the interaction between matter and energy.

Physics explains the day-to-day phenomena happening around us. It explains why lightning occurs during rainy days and why we wear light coloured cotton clothes in summer and woollen clothes in winter. It also helps us to know the working of various electrical devices, such as the incandescent bulb, fluorescent tubes and electric motors, and how X-rays can be used to detect a fracture in a bone. It explains how ventilation in a room is achieved. Chemistry deals with the transformation of substances. It classifies substances into elements and compounds. It studies the process involved when compounds are formed from elements. It also studies the decomposition of compounds into simpler substances.

Method of Application of Science

Science attempts to find the cause of an event. This is called the aim. To achieve this aim, various phenomena taking place in the inanimate and living world are observed. The reason behind a given phenomenon is determined and its correctness is verified in different situations. Science is applied through the following steps.

1. Aim: A phenomenon is chosen to determine its cause.
2. Observation: It involves noticing the phenomenon attentively in different conditions. For observation, sense organs as well as different instruments are used. In most cases, a phenomenon similar to the one observed in nature is created in the laboratory, which is called an experiment.
3. Measurement: It involves a comparison with a standard measure known as a unit. There are two systems of standard units, one is CGS (centimetre, gram, second) and the other is SI (Système International). In the CGS system, the units of length, mass and time are centimetre (cm), gram (g) and second (s), respectively, and in the SI system they are metre (m), kilogram (kg) and second (s), respectively.
4. Measurement of volume: The volume of a body is the space occupied by it. The volume of regularly shaped solid bodies can be determined easily by applying the appropriate formula. For determining the volume of an irregular solid, a measuring cylinder is used. The measuring cylinder is also used to measure the volume of a liquid.

A measuring cylinder is a cylindrical vessel with graduations in millilitre or cubic centimetre. To measure the volume of a given liquid, it is poured into an empty cylinder and the marking corresponding to the upper surface of the liquid is noted, which gives the volume of the liquid.

The volume of an irregularly shaped solid can be determined by immersing it into water contained in a measuring cylinder. For example, to measure the volume of a stone, the stone is tied with a thread and lowered into the measuring cylinder. The water level rises. The volume of the stone equals the difference between the volume of water before and after the stone is immersed.

5. Systematization: After measuring the physical quantities, they are arranged in a specific way. This is called systematization. A conclusion is then drawn after studying the measurements, which is called inference. The following table gives the CGS and SI units of some of the physical quantities.

A simple example where the method of science is applied is given below.

1. Aim: To show that the volume of a liquid displaced by a solid, which is insoluble and completely immersed in a liquid, increases with an increase in the volume of the solid.
2. Observation: Different objects, such as stone, glass and plastic, of different volumes are immersed in different liquids (taken in overflowing jars), such as water, kerosene and alcohol. The phenomenon is observed at different places and different times.
3. Measurement: The displaced liquid is collected in a beaker and its volume is measured with the help of a measuring cylinder.
4. Systematization: The volume of displaced liquid of each kind is arranged in increasing or decreasing order.
5. Inference: From studying the measurements arranged systematically, it is concluded that the liquid displaced by a solid increases with an increase in the volume of the solid. This holds good for all kinds of liquids.

Measurement of Some Physical Quantities

A physical quantity is a quantity that can be measured. A physical quantity can be quantified with the help of measurements and by assigning them units, which provide a standard for comparison.

Measurement of Mass

Mass is defined as the amount of matter contained in a body. In the SI system, the unit of mass is the kilogram (kg). The multiple units of mass are the quintal and the metric tonne, and the submultiple units are the gram (g) and the milligram (mg), where

1 quintal = 100 kg; 1 tonne = 1000 kg; 1 gram = \( \frac{1}{1000} \) kg; 1 milligram = \( \frac{1}{1000} \) g = \( \frac{1}{10,00,000} \) kg

The mass of a body does not change with place or time. It remains constant. Mass is measured by using a physical balance or a beam balance.

The weight of a body is the force of gravity exerted by the earth on it. The weight of a body depends on its mass as well as the acceleration due to gravity. The weight of a body changes from one place to another as the acceleration due to gravity on the earth changes from place to place. The weight of a body also changes with altitude, as the acceleration due to gravity changes with the altitude. The SI unit of weight is the newton (N) and the CGS unit is the dyne. One newton of force is approximately equal to the force of gravity on a body of mass 100 g. The other units of weight are called gravitational units. They are the kilogram force (kgf) and the gram force (gf).

One kilogram force is the force exerted by the earth on a body of mass 1 kg. One gram force is the force exerted by the earth on a body of mass 1 gram. The weight of a body is measured by a spring balance.

Difference between Mass and Weight

Measurement of Density

If we compare the masses of different substances of the same volume, we find the masses to be different. For example, the mass of a certain volume of iron is greater than the mass of the same volume of wood. Why is it so? This is because the atoms in iron are more densely packed than the atoms in wood. In other words, the density of iron is more than the density of wood. The density is defined as the mass per unit volume of a substance. Thus,

\[ \text{Density}\ (D) = \frac{\text{mass}\ (m)}{\text{volume}\ (V)} \]

The SI unit of density is kg m⁻³ and the CGS unit is g cm⁻³.

Determination of Density of a Solid by Using a Measuring Cylinder

Dividing the mass of a solid by its volume gives its density. The mass of a solid can be determined accurately by using a physical balance. The volume of an irregularly shaped solid can be determined by using a measuring jar (cylinder). To measure the volume of a solid, note the initial reading in the measuring jar and immerse the solid into the jar. Note down the final reading. The difference between the final and the initial readings gives the volume of the solid. Divide the mass by the volume and find out the density.

Determination of Density of a Liquid by Using a Density Bottle

A density bottle is a specially designed glass bottle available in different capacities. Generally, a density bottle of capacity 50 ml is used for finding the density of various liquids. A density bottle is a long-necked bottle provided with a ground glass stopper as shown in Fig. 1.1.

The stopper has a capillary tube. When the bottle is filled with a given liquid and the stopper is inserted, the liquid rises through the capillary tube and overflows. This ensures that an accurate volume of the liquid is taken in the density bottle whenever it is filled with different liquids. In order to find the density of a given liquid, the density bottle is washed with distilled water and dried in hot air. The mass of the density bottle with the stopper is determined by using a physical balance. The density bottle is then filled with distilled water and the stopper is inserted. The water that overflows is wiped and the mass is determined (using a physical balance). After determining the mass of the bottle with distilled water, the distilled water is poured out and the bottle is dried in hot air. Now the bottle is filled with the liquid and the stopper is inserted. The liquid that overflows is wiped out and the mass of the density bottle filled with the liquid is measured, using a physical balance.

We can find the mass of the liquid and of the distilled water by subtracting the mass of the empty density bottle from the mass of the density bottle filled with the liquid and with the distilled water. The volume of the liquid is equal to the volume of the water. Since the density of water is 1 g cm⁻³, its volume in the CGS system is equal to its mass in the CGS system. The density of the liquid can be found as follows:

\[ \text{Relative density} = \frac{\text{mass of liquid}}{\text{volume of liquid}} \div \frac{\text{mass of water}}{\text{volume of water}} = \frac{\text{mass of liquid}}{\text{mass of water}} \]

Variation in Density of Liquids and Gases with Temperature

The expansion of solids with a rise in temperature is so small that it is negligible. As the volume remains almost constant, the density of a solid (d = m/V) does not change with minor changes in temperature (from 20 °C to 40 °C). The liquids and gases, however, expand appreciably with a rise in temperature, so that the change in their density with a change in temperature is large.

Consequences of Change in Density of Liquids with Temperature

When water filled in a beaker is heated, it is hotter at the bottom than at the top. The hot water at the bottom, being lighter, rises up and the cold water at the top, being heavier, sinks in. This creates a sort of current called a convection current. The liquids heat up due to the convection current.

Consequences of Change in Density of Gases with Temperature

On being heated, gases behave in the same way as liquids. Convection currents are set up in gases also. The convection currents in gases are responsible for the formation of the sea and land breezes, the monsoon and the westerlies. The ventilation in a room is possible due to the convection current in the air. The convection current also explains why a flame points in the upward direction.

The Triangulation Method

We use the triangulation method to measure large distances, such as the distance between planets and stars, the width of a river, the height of hills, etc., where survey chains or big tapes cannot be used. Such huge distances are found out by constructing triangles, and therefore this method is known as the triangulation method. Let us see how the triangulation method can be applied to measure the distance between the corner of a table (A or B) and the toy placed on the table (C) as shown in Fig. 1.2.

Take a white sheet of paper and place it along the edges of the table. Now look at the toy (placed at C). Fix two pins on the paper at p₁ and p₂ (at the corner of the table) such that the two pins and the toy are in a straight line. Remove the two pins and join p₁ and p₂ with a straight line. Now move to the other corner of the table and place the same paper along the two edges of the table. Fix two pins (at the corner of the table) at p₃ and p₄ such that the two pins and the toy are in a straight line. Remove the pins and join p₃ and p₄. After producing, the two straight lines meet at a certain point, say p, as shown in Fig. 1.3.

Let the distance between A and B on the table be 1 m. Measure the distance between p₁ and p₃ in the diagram (Fig. 1.3). Let it be 5 cm. This implies that 1 cm length in the diagram is equal to an actual distance of 20 cm. To know the distance between you (you are at p₁) and the toy, measure the length p₁p in the diagram. To get the actual distance, multiply the length p₁p by 20 cm.

Points to Remember

1. The word science is derived from the Latin word 'scire'.
2. Physics and chemistry are the two main branches of physical sciences.
3. The main steps in the method of application of science are: (a) aim, (b) observation, (c) measurement, (d) systematization and (e) inference.
4. The volume of a body is the space occupied by it.
5. A measuring cylinder is used to measure the volume of irregular solids.
6. Mass is defined as the amount of matter contained in a body.
7. The SI unit of mass is kg. Its CGS unit is gram (g).
8. The weight of a body is the force of gravity exerted by the earth on it.
9. The SI unit of weight is newton. The CGS unit of weight is dyne.
10. Density is defined as the mass per unit volume of a substance. The unit of density in the SI system is kg m⁻³ and the CGS unit is g cm⁻³.
11. The density of a liquid is measured by using a density bottle.
12. The density of liquids and gases changes with temperature.
13. The triangulation method is used to measure large distances, such as distances between planets and stars, the width of a river, the height of hills, etc.