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.
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.
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.
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:
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 |
We need measurement because of the following reasons:
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) |
Any two advantages of SI system of unit are as follows:
We know that,
Force = mass x acceleration
= kgm/s^{2}
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 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. |
Some mechanical relations for power are as follows:
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
Solution :
2,000,000,000,
= 2 x \(10^{9}\)
= 2.6 x \(10{^-9}\)
= 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
Breadth = 155mm
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
Radius = 4cm
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:
1 \(\times\) \(10^{16}\)
= \(10^{16}\)
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
Hence, Its breadth is 36m.
Which is not true regarding SI system of measurement?
It is accepted as standard unit all over the world.
it is accepted by scientists.
It is metric system ie SI units can be expressed as powers of 100.
it is divided into fundamental unit and derived unit.
Define measurement.
The prediction of the value of quantities.
The comparison of quantities either known or unknown.
The comparison of known quantity with unknown quantity .
The comparison of unknown quantity with known quantity .
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Differences between S.I unit and Derived unit.?
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Anurag
What is 1kg mass
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