## Measurement of Some Fundamental and Derived Quantities

Subject: Science

#### Overview

Length is defined as the distance between any two points. The SI unit of length is meter. The amount of matter contained in a body is called its mass. It depend on the number of molecule and size a molecule of the body. Its SI unit is kilogram (kg). The mass of the body is measured in beam balance. This note gives us information about measurement and its types and measurement of volume and area.

#### Measurement of length

Length is defined as the distance between any two points. The SI unit of length is a meter.

One standard meter is defined as the distance between two fine lines on a platinum-iridium rod preserved at a temperature of 273.16 K and 760 mm of hg pressure.

#### Measurement of mass

The amount of matter contained in a body is called its mass. It depends on the number of molecule and size a molecule of the body. Its SI unit is kilogram (kg). The mass of the body is measured in beam balance. A balance works by measuring an object against a weight that balance another weight because the gravitational force on the is exactly the same as the gravitational force on the object being measured, that term cancels only thing being compared is the mass.

One standard kilogram is defined as the mass of a platinum- iridium cylinder of diameter equal to its height, which is preserved in a vault at International Bureau of Weights and Measures in France.

#### Measurement of time

The duration between any two events is called time. The SI unit of time is second. In a pendulum clock, the oscillation is made for the measurement of time.

One standard second is defined as the time taken by cesium -133 atom to make 9192631770 vibrations. The watch based on such vibrations is called the atomic watch. In quart watch time is measured by oscillation of pendulum and in electronic watch time is measured by frequency of alternating current. Automatic watch or mechanical watches may gain or lose time by few seconds or minutes in a day.

One second is defined as the 1/86,400th part of the mean solar day. A particular point in the space is called zenith.

A solar day is defined as the time interval between the consecutive passages of the sun through the zenith.

The time taken by earth to revolve once around the sun is called one year. Large distances such as the distance between earth and moon etc. are measured in the light year. It is the distance travelled by light in one year.

We have,

1 year = 365 days = 365 × 24h = 365 × 24 × 3600 s = 31,536,000 s
Since the speed of the light in air or vacuum is 3× 108 m/s
And distance travelled = speed × time
Therefore, 1 light year = 3 ×108 × 31,536,000 s
= 9.4608 × 1015 m

#### Measurement of Area

The space occupied by a plane surface is called area. Its SI unit is square meter (m2). If the surface area object is regular, its surface area is calculated by simple arithmetic.

Area of rectangle = length × breadth
i.e. A = l × b

Area of triangle = $\frac{1}{2}$ base × height
i.e. A= $\frac{1}{2}$ b × h

Area of circle = A=πr2
The surface area of the irregular body is determined by a graph paper method.

#### Measurement of Volume

The space occupied by a body is called volume. In SI system, the unit of volume is a cubic meter (m3). For the regularly shaped body volume of solid is determined by simple arithmetic.

Volume of rectangular parallelepiped body = length × breadth × height
i.e. V= l ×b × h

Volume of cylinder (V) = π (radius) 2 × (length)
i.e. V = π r2 l

Volume of a sphere = $\frac{4 \pi}{3}$ (radius)3
i.e. V = $\frac{4 \pi}{3}$r3=$\frac{1}{6}$ πd3 [r=d/2]
The volume of liquid or irregular shaped body is determined by using measuring cylinder. Cubic millimeter, cubic centimeter and liter are other units of volume.

##### Things to remember
• One standard meter is defined as the distance between two fine lines on a platinum-iridium rod preserved at temperature of 273.16 K and 760 mm of hg pressure.
• One standard second is defined as time taken by cesium -133 to make 91923177o.
• One standard kilogram is defined as the mass of platinum -iridium cylinder of diameter equal to its height.
• A solar day is defined as the time interval between the consecutive passages of the sun through zenith.
• The space occupied by a body is called volume. In SI system, the unit of volume is a cubic meter (m3).
• 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.
##### MEASURING TIME
Length is the distance between any two points.
SI unit = meter (m)
CGS unit = centimeter (cm)

One standard meter is defined as the distance between two fine (gold) lines on a platinum-iridium rod constructed at 0 degree C and preserved at the International Bureau of Weights and measurements in France.

To express the units of length, time and mass, we should not depend upon other units. So, they are independent.
The amount of matter contained in a body is known as mass.
SI system = kilogram (kg)
CGS system = gram (g)
1 kg mass is defined as the mass of platinum-iridium cylinder of diameter equal to its height which is preserved in the international bureau of weights and measurements in France.
A copy of original standard kg is provided to each country through which number of copies can be made and everyone can use it.
A copy of the original standard meter is available for a country which is used for developing other commercial standard meters.
The devices which are used to measure mass of an object are beam balance, top-pan balance, lever balance, etc.
One second is defined as the part of a solar day. OR,
The time taken by cesium-133 atom to make 9192631770 vibrations is called one standard second.
A solar day is the time interval between the consecutive passage of the sun through the zenith point.
Zenith is the point in the space directly above an observer standing on the earth.
 Pendulum watch Quartz watch Time taken is measured with the oscillation of pendulum bob. Time taken is measured with the oscillation of quartz crystal It is less accurate It is more accurate It works on mechanical energy It works on electrical energy
They are stop watch, wrist watch, pendulum clock, digital watch, etc.
1. 3.4 km
1 km = 1000m
3.4 km = 3.4 x 1000 = 3400m
2. 140km/hr
Here,
140 km/hr = = 38.89 m/s
3. 6 tons 20 kg
1 ton = 1000 kg
6 tons = 6 x 1000 = 6000 kg
6 tons 20 kg = (6000 + 20) kg = 6020 kg
4. 15.4 liters
1 liter = 1000 cm3 = 10-3 m3
15.4 liter = 15.4 x 10-3 m3
5. 3 weeks
1 weeks = 7 days = 7 x 24 hours = 7 x 24 x 60 minutes = 7 x 24 x 60 x 60 sec
3 weeks = 3 x 7 x 24 x 60 x 60 = 1814400sec
6. 20 hrs 55 sec
1 hr = 60 x 60 sec = 3600 sec
20 hr = 20 x 3600 = 72000 sec
20 hrs 55 sec = 72000 + 55 = 72055 sec
7. 13.6g/cm3
13.6g = 13.6 x 10-3kg
1 cm3 = 10-6 m3
Then,
13.6kg/m3 =
= 13600 kg/m3