Std-7 Sub-Physics

Chapter 1

MEASUREMENT

In this chapter you will learn

Volume and it’s unit

Vessels for measuring the volume of liquids

Measurement of volume of a liquid using

measuring cylinder and measuring beaker

Measuring the Volume of regular body

Measuring the Volume of irregular body

Area and measurement of area of regular and

irregular object

Density, it’s unit and relationship between

kg/m3 and g/cm 3

Determination of density of irregular Solid and

liquid

Introduction

Measurement is a process of comparison of unknown

quantity with a fixed known quantity of tye same kind

called the unit. The magnitude of the quantity is

expressed as,

Magnitude = Number of times the unit is contained in

the quantity × unit.

Length is the distance between two points. Its S.I.

unit is metre(symbol m). It is measured using a ruler

or a measuring tape.

Mass is the quantity of the matter contained in the

body. Its S.I. unit is kilogram(symbol kg). It is

measured using beam balance or electronic

balance.

Time is the interval of occurrence of an event. Its

S.I. unit is second(symbol s). It is measured with the

help of pendulum clock or a watch or for a short

time intervals we use stop clock or stop watch.

Temperature is a quantity which measure hotness

or coldness of a body. Its S.I. unit is kelvin(symbol)

k). Other unit are oC oF. It is measured using thermometer.

Measurement of Volume:

The space occupied by an object is called its volume.

This can be demonstrated by following activity.

S.I unit of volume:

The S.I. unit of volume is cubic metre. In short form, it is

written as m3.

One cubic metre is the volume of a cube of each side 1

metre as shown in figure below i.e., 1 m3 = 1 m × 1 m × 1

m.

Other units of volume:

• Other units of volume are units and mm3, where

1 cm3= 10-6 m3 and 1 mm3 = 10-9 m3.

• The volume of liquids is expressed in litre which is

denoted by symbol (l) and milli litre (ml).

• 1 L= 10-3 m3 = 1000cm3 and 1mL = 1 cm3

• The volume of an irregular solid is found by the

method of displacement of a liquid using a measuring

cylinder.

Relation between m3 and cm 3:

100 cm = 1 m

A cubic meter is a cube 1 meter wide, 1 meter deep and

1 meter tall.

1 m3 = 1 m x 1 m x 1 m

Substitute the conversion factor for meter to centimetre

1 m3 = (100 cm) x (100 cm) x (100 cm)

1 m3 = 1,000,000 cm3 = 106 cm3

The volume of liquid is measured generally in litre (L)

1000cm3 make one litre i.e.

1 litre= 1000cm3

Hence 1cm3= 10-3litre = 1 millilitre

Thus, 1 m3 = 1,000,000 cm3 = 106 cm3

1L= 1000 m3 = 1000mL

1mL = 1 m3 ( or 10-6 m3)

Vessels for measuring the volume of liquids

1) Measuring cylinder

It is a cylinder of generally area of cross section

of 10 cm2, made up of either glass or plastic. It

is length nearly 10cm graduated in cm3 or mL

with its zero mark at bottom and 100 marks at

the top. Thus, it is of capacity 100 cm3 (or 100

mL) as shown in figure.

The following figure(below) shows the other

kind of measuring cylinder which is used by

pharmacists to measure liquid medicines.

2) Measuring beaker:

A measuring beaker is generally used to measure

fixed volume of liquid such as milk, oil, lubricating

oil etc. Thus, they are available in different

capacities such as 50mL, 100mL, 200mL, 500mL,

1000mL. The capacity of beaker is marked on it.

Measurement of volume of a liquid

1) By using measuring cylinder

For this proceed as follow-

i) Take a measuring cylinder. wash it with water

and dry it.

ii) Place the measuring cylinder on a flate surface

and then pour the given liquid completely into

measuring cylinder gently so that no liquid

splashes out of the cylinder.

iii) Wait for some time till the liquid becomes

stationary in the cylinder. You will notice that

the meniscus(upper surface) of the liquid is

curved when the liquid becomes stationary.

iv) Read the level of the liquid in the measuring

cylinder by your eye horizontally in line with

lower surface of water as shown in the figure. In

the figure the reading is 70mL.

2) By using Measuring beaker

A measuring beaker is used to measure fixed volume of

liquid from a large volume. Suppose it required to

measure 500mL of milk from the milk contained in a

bucket.

For this, take the measuring beaker of capacity 500mL.

Wash it and dry it.

Then immerse the beaker well inside the milk contained

in the bucket so that the beaker gets filled completely

with the milk.

Take out the measuring beaker from the bucket gently so

that no milk splashes out and then pour the milk from

the from the measuring beaker into another vessel.

Measuring the Volume of regular body:

The following relations are applicable-

Volume of a cuboid (V)= length(l) × breadth (b) ×

height(h)

Volume of a cube (V)= (length)3

Volume of sphere (V)= 4/3 π × (radius)3

Volume of cylinder (V)=π × (radius) × height (h)

Volume of cone (V)=π/3 × (radius)2 × height (h)

Where π = 3.14 or 22/7

Measuring the Volume of Irregular body

The volume of a solid of irregular shape can be

measured by using measuring cylinder by the method of

displacement of liquid . This method is based on the fact

that the volume of an irregular solid is equal to the

volume of water displaced by it when it is immersed in

water. When we immerse an irregular body in water, it

displaces some amount of water. The volume of

displaced water is equal to the volume of an irregular

body that displace water.

Volume of a body of irregular shape = volume of liquid

displaced by the body when it is completely immersed

into the liquid.

This method can be used to calculate the volume of

those irregular bodies which sink in water and do not

dissolve in water.

Activity: To measure the volume of a piece of stone.

Materials Required: Measuring cylinder, water, thread, a

piece of brick

Procedure-

At first, fill the measuring cylinder partially with water.

Note down the level of the water. Let it be the initial

level of water, V1. While recording the level of water,

keep the eye in the level with the bottom of the

meniscus to avoid parallax error. After this, tie the piece

of stone with the help of thread and immerse it into the

water of measuring cylinder. We can see that, the level

of water rises. Then, note down the new level of water

carefully. Let it be the final reading, V2.

Observation

Suppose V1 is 50 ml and V2 is 75 ml.

Now,

Initial volume of water in the cylinder (V1)= 50 ml

Final volume of water in the cylinder (V2)= 75 ml

∴ Volume of the water displaced (V)=V2 -V1

= 75ml - 50ml

= 25ml

∴ Volume of the Stone= Volume of water displaced

= 25ml

Area

The total space occupied by the plane surface of the

object is known as the area of that object. The SI unit of

area is the square metre (m2). Other similar units of area

are mm2, cm2, km2, etc.

1 are= 102 m2

1 hectare= 104 m2

1 km2 = 106 m2

1 cm2 = 10-4 m2

1 mm2 = 10-6 m2

Measurement of area of regular object

There are various formulae used for the measurement of

the area of the regular plane surface. Some of them are

given below,

Area of a rectangular object (A) = length(l) × breadth(b)

∴ A= l × b

Area of a circle (A)=π×(radius)2[ π = 22/7 ]

∴ A=πr2

Area of a square (A)= (side)2

Surface area of cylinder= 2 π×(radius) ×(length)

Surface area of sphere= 4 π×(radius)2

Where π = 3.14 or 22/7.

Measurement of area of irregular object

Describe the method in steps to find the area of an

irregular lamina using a graph paper.

Graph paper : It is a sheet of paper on which horizontal

and vertical lines are ruled at regular interval of 1mm.

Area of one big square is 1 cm × 1cm = 1 cm2

Procedure : First, place the lamina over a graph paper

and draw its boundary line on the graph paper with a

pencil. remove the lamina and count and note the

number of complete squares as well as the number of

squares more than half within the boundary line (only

the squares less than half, are left while counting). The

area of lamina is equal to the sum of the area of

complete squares and the area of squares more than

half. Let n be the total number of complete and more

than half or half squares within the boundary of lamina.

Since area of one big square is 1 cm × 1cm = 1 cm2, so

the area of lamina will be n x 1cm2 or n cm2.

Density

Each body has certain mass and a definite volume.

Experimentally it is observed that

1) Equal masses of different substance have

different volume 1kg of iron and 1 kg of cotton

will have different volume and

2) Equal volume of different substance have

different masses e.g. cubes of iron and wood(1

cm × 1cm × 1cm) will weigh differently.

Definition of density

Density is defined as its mass per unit volume. It is,

essentially, a measurement of how tightly matter is

crammed together.

The symbol for density is the Greek letter ρ (called rho).

The formula for density is ρ = M/V, where ρ is density, M

is mass, and V is volume.

For better understanding-

https://youtu.be/SimFy9wOMXY

Unit of density

The SI unit of density is kilogram per cubic meter (kg/m3).

It is also frequently represented in the C.G.S. unit of

grams per cubic centimetre (g/cm3).

The relationship between S.I. and C.G.S. units

The SI unit of density is kg/m3.

The CGS unit of density is g/cm3.

Conversion from C.G.S. to S.I.

In C.G.S. unit of density = g/cm3

= 10-3kg/10-6 m3

Relationship between kg/m3 and g/cm 3

Determination of density of regular solids

The density of the solid can be determined using the

formula D = M/V.

We proceed as follows:

1) Using beam balance, measure the mass M of the

solid.

2) Using the metre ruler, measure length, breadth and

height of the regular solid and find the volume using

the relation V = length(l) × breadth (b) × height(h)

Determination of density of irregular solid

To find the density of a solid, its mass and volume are

required. The mass (M) of the solid is determined using a

physical balance. To find the volume of the solid, a

measuring cylinder with a fixed volume of water is taken

and the volume of water is noted. Let the volume of

water be V1. The solid is tied to a string and is lowered

into the measuring cylinder such that it is completely

immersed in water. The new level of water (V2) is noted.

The difference in the levels of water V = V2 – V1 gives

the volume of the solid. Knowing the mass and volume of

the solid, the density of the solid can be determined

using the formula D = M/V.

Determination of a density of a liquid:

To determine the density of solid follow the procedure

below:

1) Take a beaker. Measure the mass of empty beaker

using a common beam balance. Let the mass be

M1 gram.

2) Now take a measuring cylinder and pour milk into

to a certain level say 50mL.Thus, volume of milk,

V=50 cm3

3) Transfer the milk into empty beaker. Measure its

mass again, lets its mass be M2 gram.

4) The difference between M1 and M2 will give the

mass M of the milk. This mass of the milk M= (M2-

M1) gram. Let M=51.5 gram.

5) Calculate the density of milk using the formula:

D = M/V.

= 51.5/50 = 1.03 g/cm3

Densities of some common substances

Speed

Speed is the rate of change of position of an object with

time. The average speed of an object in an interval of

time is the distance travelled by the object divided by the

duration of the interval Hence,

Units of speed:

In S.I. system distance is measured as metre and time is

measured as second, so the S.I. unit of speed is metre

per second and sometimes it is measured in kilometre

per hour.

Relationship between km h-1 and ms-1

1 km = 1000m

1 h = 3600 s

So 1km/h = 1000/3600

or 1km/h = 1/3.6 ms-1

or 3.6 km/h = 1 ms-1

Table below gives approximate speed of some common objects

For better understanding of whole chapter:

https://youtu.be/z5LAyppdzM8

To refer textbook go through the

following pictures: