Measurement of Some Fundamental and Derived Quantities

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.