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measurement solved exercisesGroup - A
1. What is measurement?
Answer: Measurement is the process of comparing an unknown physical quantity with known physical quantity of the same kind to get accurate findings.
2. What is MKS system?
Answer: MKS system, also known as Metric System, is the system of measurement in which length, mass and time are measured in metre, kilogram and second, respectively.
3. What is fundamental unit?
Answer: Fundamental unit is the independent unit of fundamental physical quantities that has its own identity.
4. Define derived unit.
Answer: Derived unit can be defined as the unit of the derived physical quantities that depends on the fundamental units and doesn't have it's its own identity.
5. What is SI system?
Answer: SI system is the internationally accepted system of measurement, also known as the extended version of MKS system, that measures all the fundamental physical quantities.
6. What is a physical quantity? Write with examples?
Answer: Any quantity that can be measured, directly or indirectly is said to be a physical quantity. Example: time, mass, length, etc.
7. What is 'length'? Write down its SI unit.
Answer: Length is the total distance between two points.
The SI unit of Length is metre (m).
8. Define one metre length.
Answer: One metre length can be defined as the distance travelled by light in vacuum in 1/299792458 part of a second.
9. What is the mass of a body? In which units is it measured?
Answer: The total amount of matter contained in a body is called the mass of a body.
It is measured in gram (g), kilogram (kg), milligram (mg), etc.
10. Define one standard kilogram.
Answer: One standard kilogram can be defined as, "the mass of a platinum-iridium cylinder in normal atmospheric pressure kept at the International Bureau of Weights and Measures near Paris, France."
11. How is 'one second' time defined in SI system?
Answer: In SI system, 'one second' time is defined as the 1/86400th part of a mean solar day.
12. What is time? Write its SI unit.
Answer: Time is the duration between two events.
Its SI unit is second (s).
13. Define one solar day.
Answer: One solar day can be defined as the time taken by the sun to return to the zenith after one complete rotation of the Earth around the sun.
14. What is longitude?
Answer: Longitude is the imaginary line drawn on the surface of the earth, from East to West that seperated the Earth into Northern and Southern hemispheres.
15. How does quartz watch give time? Write.
Answer: Quartz watch is a digital watch. It gives time on the basis of the vibration of the quartz crystal kept inside it.
16. What is area? Write down the formula to calculate the surface area of a circular body.
Answer: Area is the total surface covered by a body.
Formula to find the surface area of a circular body is 'Ï€r²'.
17. What is 'volume of an object'? In which unit is it measured in SI system?
Answer: 'Volume of an object' is the total space occupied by the object.
In SI system, volume is measured in cubic metre (m³).
18. Write down the formula to calculate the volume of a cylindrical object.
Answer: Formula to calculate the volume of a cylindrical object is 'Ï€r²h', where Ï€ = 22/7.
19. How much time of a solar day is considered as one second?
Answer: The 1/86400th part of a solar day is considered as one second.
20. Write down the SI unit of the given physical quantities.
(i) area (ii) energy (iii) acceleration (iv) pressure (v) moment (vi) volume
Answer: The SI unit of the above-mentioned physical quantities are as follows:
(i) area = m²
(ii) energy = J
(iii) acceleration = m/s²
(iv) pressure = Pa
(v) moment = kgm²/s²
(vi) volume = m³
21. Why is International Bureau of Weights and Measures established?
Answer: The International Bureau of Weights and Measures is established to maintain uniformity in measurement system all over the world.
22. What is metric system?
Answer: Metric system is another name for MKS system that is the system of measurement in which length, mass, and time are measured in metre, kilogram and second, respectively.
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Group B
1. Mass is called a fundamental physical quantity but velocity is called a derived physical quantity. Give reason.
Answer: Mass is called a fundamental physical quantity because it does not depend on any other physical quantities and has its own identity.
We know, Velocity = Distance (Length) / Time
Since, velocity depends on two fundamental physical quantities 'Length' and 'Time', it doesn't have its own identity. So, velocity is called a derived physical quantity.
2. The unit of length is called fundamental unit but the unit of density is called a derived unit, why?
Answer: The unit of length is independent of other units and has its own identity. So, it is called a fundamental unit.
Unit of density = kg / m³
Since, unit of density depends on two fundamental units i.e. 'kg' and 'm³' and it doesn't have its own identity. So, it is called a derived unit.
3. Write any two differences between fundamental units and derived units.
Answer: Differences between fundamental units and derived units are given below:
| Fundamental Unit | Derived Unit |
|---|---|
| Fundamental units are independent of each other. | Derived units are dependent on fundamental units. |
| There are only seven fundamental units in the world. | There are hundreds of derived units in the world. |
| Some of them are: m, kg, s, etc. | Some of them are: Pa, J, kg/m³,etc. |
4. Write any two differences between fundamental physical quantities and derived physical quantities.
Answer: Differences between fundamental physical quantities and derived physical quantities are given below:
| Fundamental Physical Quantities | Derived Physical Quantities |
|---|---|
| Fundamental physical quantities are independent of each other. | Derived physical quantities are dependent on fundamental physical quantities. |
| There are only seven fundamental physical quantities in the world. | There are hundreds of derived physical quantities in the world. |
| Some of them are: length, mass, time, etc. | Some of them are: density, pressure, velocity, etc. |
5. Standard weights and scales in the market should be checked in every two years, why?
Answer: Standard weights and scales in the market should be checked every two years to ensure that they give accurate measurements. Also, to maintain uniformity in measurement in each place and protect consumer's rights, too.
6. Write any two differences between MKS and CGS system.
Answer: Differences between MKS and CGS system are given below:
| MKS system | CGS system |
|---|---|
| MKS system is also known as Metric system. | CGS system is also known as French system. |
| It is the system of measurement in which length, mass and time are measured in metre, kilogram and second, respectively. | It is the system of measurement in which length, mass and time are measured in centimetre, gram and second, respectively. |
7. Very large and very small numbers are written in the power of ten. Give reason.
Answer: Writing very large and very small numbers in the power of ten is known as scientific notation. It helps to reduce the width of the numbers without actually changing their values. And, is useful in doing easy calculation because it saves our time and space.
8. Write any two differences between mechanical clock and quartz clock.
Answer: Differences between mechanical clock and quartz clock are as follows:
| Mechanical clock | Quartz Clock |
|---|---|
| Mechanical clock gives times on the basis of oscillation of the bob (simple pendulum). | Quartz clock gives time on the basis of vibration of quartz crystals. |
| It is less accurate, comparitively. | It is more accurate, comparitively. |
9. Why is Newton called a derived unit?
Answer: We know,
Newton = kgm /s²
Since, Newton depends on the three fundamental units i.e. 'kg', 'm' and 's', and doesn't have its own identity, it is called a derived unit.
10. Quartz clock is more appropriate than mechanical clock to measure time, why?
Answer: Quartz clock measures time on the basis of vibration of quartz crystals. But, mechanical clock measures time on the basis of oscillation of a bob. The oscillation is directly affected by the climatic condition so, its measurement of time can be fluctuated. Hence, Quartz clock is more appropriate than mechanical clock to measure time.
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Group C
1. Describe the importance of measurement in our daily life.
Answer: Measurement is important in our daily life. It is useful in doing simple to complex mathematical calculations, with accuracy and efficiency. It makes trade easy. Similarly, time, length of clothes, mass of any body, etc. can be easily measured in our day to day life, with the help of measurement. So, it makes our life easy and paves path for new inventions.
2. Express the following derived units in terms of fundamental units: i) Newton ii)Pascal.
Answer: We know,
Force = mass * acceleration
or, Newton = kg * m/s²
or, Newton = kgm/s²
So, Newton can be expressed as 'kgm/s²' in terms of fundamental units.
Also,
Pressure = force / area
or, Pascal = mass * acceleration / area [force = mass * acceleration]
or, Pascal = kg * m/s² / m²
or, Pascal = kg/ms²
So, Pascal can be expressed as 'kg/ms²' in terms of fundamental units.
3. How do you measure the volume of an irregular solid? Explain.
Answer: Volume of an irregular solid is measured using liquid displacement method.
To measure the volume, water is taken in a measuring cylinder and the initial level of water is noted as A. Then, the irregular solid is dipped in the same cylinder with water in it and the new level of water is noted as B.
Finally, the volume of the irregular solid is measured as 'B-A'.
4. Express watt and joule in terms of fundamental units.
Answer: We know,
Power = Work / Time
or, Watt = force * displacement / time [ Work = force* displacement]
= mass * acceleration * m /s [ force = mass * acceleration]
= kg * m/s² * m/s
= kgm²/s³
So, Watt can be expressed as 'kgm²/s³' in terms of fundamental units.
Also,
Work = Force * displacement
or, Joule = mass * acceleration * m [ force = mass * acceleration]
= kg * m/s² * m
= kgm²/s²
So, Joule can be expressed as 'kgm²/s²' in terms of fundamental units.
5. Express the following numbers in the scientific notation.
(i) 2000085000 (ii) 0.000825 (iii) 200.82
Solution:
(i) 2000085000
= 2.000085 * 1000000000
= 2.000085 * 10⁹
(ii) 0.000825
= 825/1000000
= 8.25/1000000*100
= 8.25/10⁴
= 8.25*10^(-4)
(iii) 200.82
= 2.0082 * 100
= 2.0082 * 10²
6. Convert the following scientific notations into the general form.
(i) 3*10⁸ (ii) 1.5*10^(-5) (iii) 2.57*10^(-7)
Solution:
(i) 3*10⁸
= 3 * 100000000
= 300000000
(ii) 1.5*10^(-5)
= 1.5 /10⁵
= 1.5 /100000
= 0.000015
(iii) 2.57*10^(-7)
= 2.57/10⁷
= 2.57/10000000
= 0.000000257
7. Convert the following:
(i) 54 km into cm
Solution:
We know,
1km = 10⁵cm
So, 54km = 54*10⁵cm
= 5.4*10⁶cm
(ii) 2mm² into m²
Solution:
We know,
1mm² = 10^(-6)m²
So, 2mm2 = 2*10^(-6)m²
8. The volume of water in a measuring cylinder is 50ml. When a piece of stone is immersed in the cylinder, the volume of water increases to 87.3 ml. Calculate the volume of the stone.
Solution:
Given,
Volume of water in measuring cylinder (A) = 50ml
Volume of water and stone in measuring cylinder (B) = 87.3 ml
We know,
1ml = 1 cm³
Now, volume of stone = B - A
= 87.3 - 50
= 37.3 ml
= 37.3 cm³
Hence, the volume of the stone is 37.3 cm³.
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Group D
1. What is the advantage of scientific notation or standard notation? Explain.
Answer: Scientific notation or standard notation refers to expressing long digit numbers in terms of power of 10. It saves our space and time, both. Writing very long numbers every time might be boring as well as it has high chances of error. But, when we write them in scientific notation, the digits look precise, has less chances of error and makes calculation easier.
2. The diameter of a football is 12m. Calculate it s volume.
Solution:
Given,
Diameter of a football (d) = 12m
Volume of the football (V) = ?
We know,
Volume of a sphere (football) = Ï€d³/6
= 22/7 * (12)³ /6
= 905.142 m³
Hence, the volume of the football is 905.142 m³.
3. Calculate the volume of each figures from the given measurements.
(i) Cuboid (l,b,h) = (10cm,5cm,2m)
Solution:
Given,
Length of a cuboid (l) = 10cm
Breadth of a cuboid (b) = 5cm
Height of the cuboid (h) = 2m = 2*10²cm
Volume of the cuboid (V) =?
We know,
Volume of a cuboid (V) = l*b*h
= 10*5*2*10²
= 1000cm³
= 10⁴ * 10^(-6) m³
= 1* 10^(-2) m³
Hence, the volume of the given cuboid is 1*10^(-2)m³.
(ii) Cylinder (r=8cm, h=12cm)
Solution:
Given,
Radius of the cylinder (r) = 8cm
Height of the cylinder (h) = 12cm
Volume of the cylinder (V) = ?
We know,
Volume of the cylinder = Ï€r²h
= 22/7 * 8² * 12
= 2413cm³
= 2.413 *10³ cm³
Hence, the volume of the cylinder is 2.413*10³cm3.
4. How is the volume of an irregular solid measured? Explain with neat figure.
Answer: Volume of an irregular solid is measured using liquid displacement method.
 |
| Source: Wikipedia (Displacement of stone in water) |
As shown in the above figure, first of all, the initial level of water in the measuring cylinder is noted down as 'A'. Then, the level of water with solid is measured and noted as 'B'.
To find the volume of the irregular solid, the reading of A is subtracted from the reading of B. Then, we receive the volume in ml or l.
Then, using 1ml = 1cm³, we find the volume of an irregular solid.
5. Name the four systems of unit and explain any two of them.
Answers: The four systems of unit are:
1. MKS system
2. CGS system
3. FPS system
4. SI system
Explanation of any two systems of unit are:
FPS system:
FPS system, also known as British System, is the system of measurement in which length, mass and time are measured din Foot, Pound and Second, respectively.
SI system:
SI system, also known as the extended version of the MKS system, is internationally accepted system of measurement in which all the physical quantities can be measured.
Questions in this article have been taken from 'Oasis School Science - Grade 9', published by Oasis Publication (P) Ltd. Author of this book is Jayananda Kapadi and the Editor is Dr. Rameshwar Adhikari.
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