## Measurement

Subject: Science

#### Overview

Measurement is defined as the comparison between unknown quantities with known quantities. The reference standard with which we carry out measurement of physical quantity is called unit. This note provide further information about measurement and units.
##### Measurement

Measurement is defined as the comparison between unknown quantities with known quantities of the same kind. To approach the subject quantitatively, it is essential that we make measurements.

A physical quantity is that which can be measured directly or indirectly. Mass, length, time, density, etc. are some examples of the physical quantity.

The measurement of unknown quantity can be done by comparing it with a standard quantity of the same kind. Thus, the comparison of an unknown quantity with a known quantity with a known or standard quantity is called measurement.

#### Importance of Measurement

• Measurement is essential in selling and buying goods.
• It is essential in performing scientific experiments to establish the truth about a physical phenomenon.
• It is required for the global understanding of the quantity of a substance.
• It is essential in performing the experiment for making our daily food.
• Measurement of the medicine is a must in the treatment of diseases.

#### Fundamental quantity and derived quantity

Those physical quantities, which can neither be derived from others nor be further resolved into simpler quantities, are called fundamental quantities. Length, mass, and time are the fundamental quantity. And the units of fundamental quantities are called fundamental units or basic units.

For example length of the body is a fundamental quantity as it cannot be expressed in terms of other quantity.

Those physical quantities, which depend on two or more fundamental quantities or power of a fundamental quantity, are called derived quantities. And the units of derived quantities are called derived units.

For example, Area is a derived quantity. Since area= l × b, so it depends on the power of length.

#### Unit

The reference standard with which we carry out the measurement of any physical quantity of the same kind is called unit. For example, the meter is the unit of length and kg is the unit of mass.

#### Standard system of units

In Nepal, some people still use the local units like haat and mana for measurement of length and mass. These units may vary from place to place. So, in order to maintain the uniformity in measurement of physical quantities, the following standard units are used:

• MKS system: In this system, mass, time, and length are measured in a kilogram, second and meter respectively. It is also known as the metric system.
• CGS system: In this system, length is measured in centimeter, mass in gram and time in second.
• FPS system: In this system, length, mass, and time are measured in foot, pound and second respectively.
• SI system: It is the most important system of units. It is also the improved version of the MKS system. Simply put, a system of physical based on the meter, kilogram, second, ampere, kelvin, candela, and mole, together with a set of prefixes to indicate multiplication or division by a power of ten is known as the SI system. It can be divided into two groups; fundamental unit and derived unit.

#### Fundamental quantities and their units

 Fundamental quantity Unit Symbol Length Meter m Mass Kilogram kg Time Second s Temperature Kelvin K Electric current Ampere A Luminous intensity Candela cd Amount of substance Mole mol

#### Advantages of International System over other System of Units

• The International system is the rational system of units. That is, this system makes use of only one unit for physical quantity.
• It is a coherent system of units. That is, in this system, all the derived units can be easily obtained from fundamental units.
• It is a metric system that multiplies and sub-multiplies can be expressed as powers of 10.
##### Things to remember
• Measurement is defined as the comparison between unknown quantities with known quantities.
• The reference standard with which we carry out measurement of physical quantity is called unit.
• Those physical quantities, which can neither be derived from others nor be further resolved into simpler quantities, are called fundamental quantities.
• Those physical quantities, which depend on two or more fundamental quantities or power of fundamental quantity, are called derived quantities.
• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.
##### SI System and Metric Units
Measurement is the process of comparing unknown quantity with a known quantity.
We need measurement because of the following reasons:
1. To approach the subject quantitatively
2. While selling or buying goods
3. During construction
4. For research
The quantity which can be measured directly or indirectly is known as physical quantity. Example: length, mass, time, force, etc.
Unit is the reference standard with which we carry out the measurement of a physical quantity.
Traditional units like palm, bitta differs from person to person leading to no uniformity in measurement.
Fundamental quantities are those physical quantities which can neither be derived nor be resolved into other simpler quantities.
 Fundamental quantity Unit Length M Mass Kg Time Second (s) Temperature Kelvin (K) Amount of substance mol (mole) Luminous intensity cd (candela) Electric current A (Ampere)
Those units which are independent with each other and can not be resolved into other units are called fundamental units.
The units which depend upon two or more fundamental units are called derived units. For example: speed (m/s), force (N)
It is the system of measurement where mass is measured in kilogram (kg), length in meter(m ) and time in second(s).
The system of unit in which length is measured in centimeter, mass in gram and time in second is known as CGS system.
One advantage of MKS over CGS is MKS is used all over the world.
SI system of unit is the improved and extended version of MKS system which is internationally accepted.
Any two advantages of SI system of unit are as follows:
1. It gives one unit for one physical quantity.
2. It provides uniformity in measurement.
We know that,
Force = mass x acceleration
= kgm/s2
Unit of force is a combination of three fundamental units. So, it is a derived unit.
Pressure = = This shows that pascal is derived from fundamental quantities kg, m and s. So it is a derived unit.
It is the SI unit of frequency which is derived from 'second'. So, it is a derived unit.
 Fundamental units Derived units They are independent to the other units. They are dependent to fundamental units. There are seven fundamental units. Except those 7, all are derived units. Example: meter (m), kilogram (kg), For example: Pascal (Pa), Newton (N), etc.
The unit which does not depend upon other unit is known as basic unit. SI system is developed to bring uniformity and similarity in the system of measurement as different systems were found to be prevalent in different countries, creating problem for people.
 SI unit MKS unit It is an extension of MKS system. It is the system where length is measured in meter, mass in kg and time in second. It has brought uniformity in measurement. It could not bring similarity in the measurement.
The original platinum-iridium rod which is in France is called primary standard and its copies are known as secondary standard.
Amount of substance = mole (mol)
Unit of current = Ampere (A)
The duration between any two events is called time. Its SI unit is second.
The differences between work and power are as follows:
 Work Power It is the product of force and displacement in the direction of force. It is the rate of doing work Mathematically, W = F x d Mathematically, P = Its SI unit is Joule Its SI unit is Watt. It does not depend upon time. It depends on time.

The relation between the horsepower (hp) and watt (W) is
1 hp = 746 Watt

=750 Watt (approx)

Some mechanical relations for power are as follows:
1. P =
2. P =
3. P = F x v ( v = velocity)
4. P =
The comparison of unkown quantity with known standard one is called measurment.

Solution
(a) 500 mm = 500 /10 = 50 cm [10mm=1cm]

(b) 500 mm = 50
= 500/100 = 5m = 5x$10^{-2}$ [100cm=1m]

(c)500 mm = 5x$10^{-2}$m
= 5x$10^{-2}$m / 1000 km = 5x$10^{-6 }$ [1000m=1km]

10 kg = 10x1000 = 10000g= 1x $10^{4}$ [1000gm=1kg]

Hence, 10 kg equals 1x $10^{4}$

2 hours, 10 minutes and 40seconds
= 2 x 60min+10min+40 s
= 120 min + 10min+40 s
= 130 x 60s + 40s
= 7800 + 40 s
= 7840 s
= 7.84 x $10^{3}$ s

Hence, 2hr , 15 min and 30 sec equals 7.84 x $10^{3}$ sec

= 2 x 2.5 x $10^{6}$ x $10^{-3}$

= 5.0 x $10^{6-3 }$

= 5 x $10^{3}$

= 3.5 x $10^{12}$ x $10^{-3}$ x $10^{-3}$ x $10^{-3}$ x $10^{-3}$$km^{2}$ [1km= $10^{3}$m]

= 3.5$km^{2}$

Thus, 3.5 x $10^{12}$$mm^{2}$ is equal to 3.5$km^{2}$ .

= 4.91 x $10^{4}$ x $10^{3}$ x $10^{3}$ x $10^{3}$$m^{3}$
= 4.91 x $10^{13}$ x $10^{2}$x $10^{2}$ x $10^{2}$ x $cm^{3}$
= 4.91 x $10^{19}$$cm^{3}$

Thus, 4.91 x $10^{4}$$km^{3}$ is equal to4.91 x $10^{19}$$cm^{3}$

Given,
Diameter of the volleyball (d) = 80cm
Radius of the volleyball (r) = $\frac{80}{2}$ = 40cm = 0.4m
Volume of the volleyball (V) = ?

We know that,
V = $\frac{4}{3}\ \pi\ r^{3}$
= $\frac{4}{3}\ \times$ $\frac{22}{7}$ $\times$ [ 0.4$^3$ ]
= $\frac{5.632}{21}$
= 0.271
= 2,71 $\times$ $10^{-2}$ m$^3$

Hence, the volume of the volleyball is 2,71 $\times$ $10^{-2}$ m$^3$

Here.

Length = 22mm
Height = 10mm
We Know
Volume of rectangular Object = L $\times$ B $\times$ H
= 22 $\times$ 155 $\times$ 10
= 3.41 $\times$ $10^5$ $m ^ -5$

Again,

Area of book = Length $\times$ breadth
= 3.41$\times$ $10^{-3}$ $m ^2$

Hence, the volume of the book is 3.41 $\times$ $10 ^5$ $m^{-5}$ and the area os each sheet is 3.41$\times$ $10^{-3}$ $m^2$.

given,
Length = 50cm

We know,
Volume of Cylinder = π(radius)$^2$ $\times$ (length)
= 3.14 x 4$^2$$\times$ 50
= 2512

Solution ;
512mm = 51.2 cm

= $\frac{51.2}{100}$ m = 0.512m = 5.12 $\times$ $10^{-2}$m

Thus 512m = 5.12 $\times \;10^{-2}$m

Solution ;

1hour = 60min
$\therefore$ 1 hour = 3600 sec

Now,
3600 $\times$ 4.6
= 16560s

$\therefore$ 4.6 hours =16560s

Solution;
12kg = 12 $\times$ 1000g
= 12000g
= 1.2 $\times$ $10^{4}$ g [$\therefore$1000gm = 1kg]

Hence, 12kg equals 1.2 $\times$ $10^{4}$ g

Solution:

Now,
1kg = 1000000mg

So,
= $\frac{120}{1000000}$
= 1.2 $\times$ $10^{-5}$kg

$\therefore$ 120 milligrams equals 1.2 $\times$ $10^{-5}$kg

Solution:
1min= 60 seconds
1hr = 60 minutes
So,
50 hours = 50 $\times$ 60 (\times\) 60

= 180000S

$\therefore$ 50 hours equals 180000Seconds.

Solution:

1kg = 1000g
6.2 x 1 kg = 6.2 x 1000 g {Multiplying both sides by 6.2}
6.2 kg = 6200g

Solution :

1 $\times$ 1. $10^{10}$ = 1. $10^{10}$

Solution:
= 2.3 $\times$5 $\times$ 10 $^7$ $\times$ $10^{-2}$

= 1.15 $\times$ $10^{6}$

Solution:

Here,
Area of room = 36$m^{2}$
Length of room = 6m

We know that,
Area of rectangular room = L $\times$ B

or, 36 = 6 $\times$ b
or, b = $\frac{36}{6}$
or, b = 36m