## Chapter 1 Measurement Synopsis

A **Physical Quantity** is one which is related to a material body or an event that can be measured directly or indirectly.

**Example:** mass, length, time, velocity, force etc. are examples of some physical quantities.

**Physical Quantities Are Of Two Types-**

- scalar quantity and
- vector quantity.”

1. The physical quantities which have only magnitude but no direction are called scalar quantities.

**Example:** length, mass, time, temperature, density, volume, work, energy etc.

**Read and Learn More WBBSE Solutions for Class 9 Physical Science and Environment**

2. The physical quantities which have both magnitude and direction are called vector quantities.

**Examples:** displacement, velocity acceleration, linear momentum, force, electric field etc.

Electric current intensity have both magnitude and direction but it does not obey ‘vector rules’ and hence it is not a vector quantity.

The **Fundamental Units** are the units of the physical quantities, which are not dependent on any other units, and all other units are derived from them.

In the international system of units (SI system) the **Seven Fundamental Units Are-**

Units which are derived from one or more, than one fundamental unit are called derived units.

**For Example** area, volume, speed, velocity, acceleration, force, momentum, etc. are derived units.

Unitless physical quantities are defined as the ratio of the same units of two different physical quantities.

**Examples:** atomic weight, molecular weight, relative density, refractive index, relative humidity etc.

A dimensionless physical quantity may have a unit but a unitless physical quantity is always dimensionless. (example plane angle = \(\frac{length of arc}{radius}\) i.e, dimensionless but have a unit (radian in SI)

**SI Unit** of length is metre-The metre is the distance travelled by light in second in \(\frac{1}{299792458}\) vacuum.

**Unit Of Time** is second in SI-the second is the duration of 9192631770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground states of the cesium-133 atom.

The amount of space occupied by a body is its volume.

**Unit Of Volume In CGS System:** cm³ and in Sl: m³, 1m³ 10^{6 }cm³ another unit: litre. The volume of 1 kilogram of pure water at 4°C is called 1 litre.

1L = 1000 cm³ and 1m³ 1000 L

The density of a substance is its mass per unit volume.

M The formula for density is d = \(\frac{m}{v}\) where d is V’ density, M is mass and V is the volume of a substance.

**Units Of Density:** In CGS system: g/cm³ and in Sl: kg/m³

**Units For Measurement Of Very Small Distances Are:**

**Micron (u):**1 micron = 10^{-6}metres. The size of microscopic objects is expressed in micron units.**Angstrom (Å):**1 angstrom 10^{-10}metre. The wavelength of light and distance between atoms in a crystal are expressed in angstrom unit.**X-unit:**1 X-unit 10^{-13}metre. The diameter of an atom is expressed in X-unit.**Fermi:**1 Fermi 10^{-15}metre. The diameter of the nucleus of an atom is expressed in fermi.

**Units For Measurement Of Very Large Distances Are:**

**1. Astronomical Unit (AU):** The average distance between the sun and the earth is called 1 AU. 1AU 1.496 x 10^{11} metre.

**2. Light Year:** The distance that is traversed by light in a vacuum in one year is called one light year. One light year = 9.46 x 10^{12}km. The unit light year is used to express the distance between stars, the size of a galaxy etc.

**3. Parsec:** One parsec is the distance of an astronomical object from the sun that has a parallax angle of one arc second (1 degree = 60 minutes, 1 minute = 60 seconds).

1 parsec 3.26 light year = 3.08 x 10^{13} km. Parsec is the largest unit of length.

**Some Very Small And Very Large Units For The Measurement Of Masses Are**

**1. Atomic mass unit (amu or u):** 1 amu or u = 1 Da = 1.66054 x 10^{-27}kg.

The atomic mass unit is used for the measurement of masses of molecules or atoms.

**2. Carat:** 1 carat = 200 mg = 0.2 g. Carat is used as the unit of measurement for masses of gold, diamond etc.

**3. Quintal:** 1 quintal (q)= 100 kilogram.

**4. Metric Ton:** metric ton = 1000 kilogram.

**5. Chandrasekhar Limit (CSL)-1** Chandrasekhar limit = 1.39 x mass of the sun = 2.765 x 10^{30}kg.

**Measurement Of Small Area:**

**Barn (b)** is used to measure a very small area. It is approximately equal to the area of the cross-section of the nucleus.

1 b = 10^{-28}m^{2}

## Chapter 1 Topic A Measurement And Units Short And Long Answer Type Questions

**Question 1. What is a physical quantity? Give some examples.**

Answer: Any natural event or phenomenon that can be measured directly or indirectly is called a physical quantity.

**Example:** Length, mass, temperature, work, acceleration, velocity, force, displacement etc. are physical quantities.

**Question 2. Can all natural phenomena be termed as physical quantities? Explain with examples.**

Answer: We observe different natural phenomena in our day-to-day life and feel them. But all of them cannot be quantified by measurement.

**Examples:** Anger, affection, charity etc.

Since all these natural phenomena cannot be measured, they are not called physical quantities.

**Question 3. What is a scalar quantity? Give some examples of scalar quantities.**

Answer: Those physical quantities which have only magnitude but no direction are called scalar quantities.

**Example:** Length, mass, work, temperature etc. are scalar quantities.

**Question 4. What is a vector quantity? Give some examples of vector quantities.**

Answer: Those physical quantities which have both magnitude and direction and whose addition follows the rules of vector addition are called vector quantities.

**Example:** Displacement, velocity, acceleration, force etc. are vector quantities.

**Question 5. Write the differences between scalar and vector quantities in a tabular form.**

Answer: The differences between scalar and vector quantities:

**Question 6. If any physical quantity has both magnitude and direction, can it be called a vector quantity? Or, Electric current has both magnitude and direction. Then why is it called a scalar quantity?**

Answer: Any physical quantity having magnitude and direction cannot necessarily be called a vector quantity. For example, electric current.

Electric current has both magnitude and direction, but the addition of electric current does not follow the rules of vector addition. Hence, electric current is not a vector quantity but a scalar quantity.

**Question 7. Mention which one is scalar and which one is vector among the following quantities: length, time, mass, weight, force, speed, velocity, acceleration, momentum, work, power, pressure, displacement, frequency, and density.**

Answer:

**Scalar Quantity:**

Length, time, mass, speed, work, power, pressure, frequency, density.

**Vector Quantity:**

Weight, velocity, acceleration, force, momentum, displacement.

**Question 8. What is unit?**

Answer: While measuring any physical quantity, some convenient and definite quantity of it is taken as a standard and then the whole physical quantity is measured in terms of the standard. This standard is called one unit.

**Question 9. What is the necessity of a unit?**

Answer: In a scientific experiment, it is necessary to mention measurements accurately. So, a unit is essential while measuring any physical quantity. Any physical quantity is expressed in terms of a numerical number and its unit.

Measurement is not possible without a unit. Unit is also necessary for establishing relationships among different physical quantities and verifying the correctness of the equations involving physical quantities.

**Question 10. What is the primary or fundamental or base unit? What are the primary units in SI?**

Answer: Fundamental or primary unit is a set of units used in the measurement of physical quantities from which other units can be derived. Primary units or base units are independent of each other.

In SI, length, mass, time, temperature, electric current, luminous intensity and amount of substance are represented by metre, kilogram, second, kelvin, ampere, candela and mole, respectively.

**Question 11. Why are the units of length, mass and time called fundamental units?**

Answer: Units of length, mass and time are called fundamental units because

- Units of length, mass and time are independent of each other;
- One cannot reduce them further into more simple units;
- With the help of these three units, one can fundamental units. form units of other physical quantities.

**Question 12 What is a derived unit? Explain with examples.**

Answer: A unit of measurement that is formed by combining one or more fundamental units is called a derived unit.

**Example:** Units of velocity, acceleration, momentum, force, work etc. are derived units. displacement time

Therefore, a unit of velocity is made up of a unit of length and a unit of time. So, it is a derived unit.

**Question 13. Distinguish the units of the following quantities into fundamental and derived units: area, volume, displacement, velocity, acceleration, force, work, energy, power, momentum, mass, weight, height, density, wavelength, and time period.**

Answer:

**1. Quantities With The Fundamental Unit:** Displacement, mass, height, wavelength, and time period.

**2. Quantities With The Derived Unit:** Area, volume, velocity, acceleration, force, work, energy, power, momentum, weight, and density.

**Question 14. Give an example of a derived unit formed by two fundamental units.**

Answer: A unit of speed is a derived unit formed by two fundamental units.

Unit of speed =

∴ unit of speed is a derived unit formed by the two fundamental units of length and time.

**Question 15. Give an example of a derived unit which is formed by three fundamental units.**

Answer: A unit of force is a derived unit formed by three fundamental units

∴ unit of force is a derived unit formed by three fundamental units of length, mass and time.

**Question 16. What is a system of units? What are the advantages of a system of units?**

Answer: A system of units is a set of all the fundamental and derived units that constitute the units of all physical quantities.

The introduction of a system of units has not only helped the scientific community but also removed the difficulties of maintenance of accounts in our daily lives.

Saying that a table has a length approximately equal to four cubits does not signify its correct length. But if it is said that its length is 1.5 m, we get a correct idea about its length.

**Question 17. Why CGS system or SI is called a metric system?**

Answer: CGS system or SI is called a metric system because to convert any physical quantity from any definite unit to another smaller or larger unit in these systems, one has to only shift the decimal point.

**Example:** 500 cm = 5m = 5000 mm = 0.005 km. No multiplication or division is necessary for this conversion.

**Question 18. What are the advantages of the metric system? **

Answer:

**The Advantages Of The Metric System Are:**

- The metric system is based on powers of 10. So, it is easier to convert units of any physical quantity simply by moving the decimal points.
- Once the meaning of the prefixes is remembered, one can easily convert mass, distance, and volume measurements. No further conversion factors are to be memorised except the power of 10.
- There is a convenient relationship between mass and volume in this system. For example, the mass of 1 cm3 of water is 1 g or the mass of 1 L of water is 1 kg (at 4°C).

**Question 19. What is a unitless quantity? Give example.**

Answer: If a physical quantity is the ratio of two physical quantities with the same unit, then that physical quantity has no unit. This type of physical quantity is called unitless quantity.

**Example:** Atomic weight, specific gravity, molecular weight, strain etc. are unitless quantities.

Hence, atomic weight and specific gravity are both the ratios of two quantities of the same nature (here, mass). Hence, these physical quantities are unitless.

**Question 20. Define the unit of length in Sl.**

Answer; The Unit of length in SI is metre (m). One metre (m) is the distance which is traversed by light in \(\frac{1}{299792458}\) vacuum in a second.

**Question 21. Define the unit of time in SI.**

Answer: The unit of time in SI is second (s). One second is the duration of 9192631770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of the ^{133}Cs atom.

**Question 22. Names of some ‘lengths’ and some ‘units’ are given below. You have to write which unit is used generally for the measurement of a particular length. Lengths: Wavelength of light, the diameter of an atomic nucleus, size of a galaxy, the diameter of an atom, the average distance of the earth from the sun, size of a microscopic object. Units: Astronomical unit (AU), angstrom (A), light year, fermi, X-unit, micron.**

Answer: The given lengths and their units are written in the following tabular form.

**Question 23. What do you mean by 1 solar mass?**

Answer: Solar mass is a large unit of mass used in astronomy. Masses of galaxies, nebulae and stars are expressed with the help of this unit.

**Question 24. What is the difficulty of expressing the mass of an elephant (6000 kg approximately) in terms of atomic mass units?**

Answer: Atomic mass unit is generally used to measure the masses of very small particles like molecules and atoms because 1 atomic mass unit (amu or u) = 1.66054 x 10^{-27}kg.

In this case, the mass of the elephant is 6000 kg. If this is expressed in u, its value becomes

= 6/166054 x 10 ^{25
} = 0.000036133 x 10^{25}

= 3.5 x 10^{20 }u (approx)

As this figure is a very large amount, it is impractical to work with it. For this reason, the mass of an elephant is not expressed in terms of u.

**Question 25. What do you mean by the volume of a body? Is there any difference between this volume and the volume of the material of the body?**

Answer: The volume of a body is the amount of space occupied by it.

**The volume of the material of the body**

If a solid body is made up of a single material, then its volume is the same as the volume of its material. But the volume of a hollow body made up of only one material is greater than the volume of its material.

**Question 26. What are the units of volume in the CGS system and SI? Write the relationship between these two units. **

Answer: The unit of volume in CGS system and Sl are cm^{3} and m^{3}, respectively.

The relationship between them is 1m^{3} (100 cm)^{3} = 106 cm^{3}.

**Question 27. Define litre. 1 litre = how many cm3 ?**

Answer: One litre (1 L) is defined as the volume of 1 kilogram of pure water at 4°C or 277 K.

1L = 1 dm^{3} = (10 cm)^{3} = 1000 cm^{3}.

**Question 28. Why is 4°C or 277K mentioned in the definition of a litre? Establish a mathematical relationship between the density of a body and its mass and volume.**

Answer: The temperature of 4°C or 277 K is mentioned in the definition of litre because in general, the volume of a liquid increases and its density decreases with the rise of temperature. But in case of water, there is an exception to this rule for 4°C.

If the temperature between 0°C and the temperature of water is increased from 0°C, its volume decreases and density increases. This process goes on up to a temperature of 4°C. At 4°C, the density of water is 1g/cm^{3} and is maximum.

After 4°C, if the temperature is increased, the volume of water increases and its density decreases. So at 4°C, volume of 1000 g or 1 kg of water is 1000 cm^{3} or 1 L.

Let the mass and volume of any body be m and V, respectively.

∴ mass of unit volume = \(\frac{m}{v}\)

∴ density of the body, d = \(\frac{m}{v}\)

This is the required relationship.

**Question 29. What is density? What are the units of density in CGS system and SI? Establish a relationship between these two units.**

Answer:

The density of a material is defined as its mass per unit volume.

Units of density in CGS system and Si are g/cm^{3} and kg/m^{3}, respectively.

The relationship between them is

or, 1 g/cm^{3} = 1000 kg/m^{3}

**Question 30. How does the density of a material change with the increase of temperature?**

Answer: The density of a material decreases with an increase of temperature. However, the density of water increases when the temperature is increased from 0°C to 4°C.

**Question 31. What is the mean solar day? Write its value in seconds.**

Answer: The average of solar days for one year is a mean solar day.

**Mean Solar Day**

Value of 1 mean solar day = 86400 seconds.

## Chapter 1 Topic A Measurement And Units Very Short Answer Type Questions Choose The Correct Answer

Question 1. Which of the following is the largest unit for measurement of length?

- Light Year
- Kilometre
- Parsec
- Metre

Answer: 3. Parsec

Question 2. Which of the following is not a physical quantity?

- Velocity
- Mass
- Displacement
- Anger

Answer: 4. Anger

Question 3. Which of the following is a physical quantity?

- Anger
- Affection
- Speed
- Frustration

Answer: 3. Speed

Question 4. Unit of which of the following quantities is different from the others?

- Pressure
- Stress
- Coefficient Of Elasticity
- Force

Answer: 4. Force

Question 5. Which of the following is a scalar quantity?

- Momentum
- Work
- Weight
- Force

Answer: 2. Work

Question 6. Unit of which of the following quantities is made up of two fundamental units?

- Force
- Momentum
- Acceleration
- Work

Answer:

Question 7. Unit of which of the following quantities is made up of three fundamental units?

- Velocity
- Acceleration
- Speed
- Momentum

Answer: 2. Acceleration

Question 8. Unit of which of the following quantities is made up of four fundamental units?

- Force
- Specific Heat
- Power
- Heat Capacity

Answer: 4. Heat Capacity

Question 9. The wavelength of a light ray is 6000Å. What is the value of this wavelength in ‘m’ unit?

- 6 x 10
^{-7} - 6 x 10
^{-6} - 6 x 10
^{-8} - 6 x 10
^{-10}

Answer: 1. 6 x 10^{-7}

Question 10. The distance from a point at which a length of 1 AU forms an angle of one second at that point is

- 4.26 light year
- 3.26 light year
- 2.26 light year
- 5.26 light year

Answer: 2. 3.26 light year

Question 11. The length, breadth and height of a water tank are 3m, 2m and 1 m, respectively and the tank is half-filled with water. What is the volume of water contained in the tank?

- 6000 L
- 3000 L
- 30000 L
- 60000 L

Answer: 3. 30000 L

Question 12. What is the temperature at which the density of water is maximum?

- 0°C
- 4°C
- 8°C
- 10°C

Answer: 2. 4°C

Question 13. The density of iron is 7.8 g/cm3. What is the mass of 100 cm3 of iron?

- 0.78 kg
- 7.8 kg
- 0.078 kg
- 78 kg

Answer: 1. 0.78 kg

Question 14. Select one scalar quantity and one vector quantity from the following whose units are derived from three fundamental units

- Speed, velocity
- Work, acceleration
- Work, force
- Power, acceleration

Answer: 3. Work, force

Question 15. Steradian is the unit of

- Angle
- Solid angle
- Arc of a circle
- Circumference

Answer: 2. Solid angle

Question 16. Which of the following quantities is not a physical quantity?

- Length
- Water
- Force
- Time

Answer: 2. Water

Question 17. Which of the following units is a derived unit?

- Mole
- Cubic metre
- Ampere
- Light year

Answer: 2. Cubic metre

Question 18. Unit of volume is

- Mole
- Kilogram
- Litre
- Square Metre

Answer: 3. Litre

Question 19. The temperature at which the volume of 1 kg of water is considered to be 1L is

- 0°C
- 10°C
- 4°C
- 100°C

Answer: 3. 4°C

Question 20. The unit which is convenient for the measurement of the diameter of molecules and atoms is

- Micron
- Metre
- Parsec
- Light Year

Answer: 1. Micron

Question 21. One nanosecond is equal to how many seconds?

- 10
^{-3} - 10
^{-5} - 10
^{-9} - 10
^{-12}

Answer: 3. 10-9

Question 22. One part of how many parts of an average solar day is considered to be one solar second?

- 84600
- 86400
- 8640
- 365

Answer: 2. 86400

Question 23. Which of the following is a larger unit used for the measurement of mass?

- Kilogram
- Quintal
- Carat
- Gram

Answer: 2. Quintal

Question 24. 1 nm = how many metres?

- 100
- 1000
- 10
- 10-9

Answer: 4. 10-9

Question 25. Unit of temperature in SI

- Degree Celsius
- Candela
- Kelvin
- Mol

Answer: 3. Kelvin

Question 26. Mass of 5 cm3 of water at 4°C is

- 5g
- 5 kg
- 0.5 g
- 50 kg

Answer: 1. 5g

Question 27. The unit which is used to measure the distance between stars is

- Angstrom
- AU
- X-unit
- Fermi

Answer: 2. AU

Question 28. What is the relationship between the mass m, the density d and the volume V of an object?

- mdV = 1
- md = V
- \(\frac{m}{v}\) = d
- \(\frac{v}{m}\) = d

Answer: 3. \(\frac{m}{v}\) = d

Question 29. The cross-sectional area of the nucleus of an atom is x barn. Its value in m2 units is

- X x 10
^{-24} - X x 10
^{-28} - X x 10
^{-26} - X x 10
^{-30}

Answer: 2. X x 10^{-28}

Question 30. One ring is made up of 10-carat gold. What is the mass of gold in g unit?

- 4
- 2
- 20
- 0.2

Answer: 2. 2

Question 31. The length of a bacteria is 3 microns. The length of the bacteria in m unit is

- 3 x 10
^{-13} - 3 x 10
^{-6} - 3 x 10
^{-5} - 3 x 10
^{-7}

Answer: 2. 3 x 10^{-6}

Question 32. The wavelength of the yellow light of Na has a wavelength of 592 nm. In Å unit the wavelength is

- 59.2 Å
- 5920 Å
- 59200 Å
- 5.92 Å

Answer: 2. 5920 Å

## Chapter 1 Topic A Measurement And Units Answer In Brief

**Question 1. What are the types of physical quantities?**

Answer:

**Physical Quantities Are Of Two Types:**

- scalar and
- vector.

**Question 2. State whether the barn is a fundamental unit or a derived unit.**

Answer: Barn is a derived unit.

**Question 3. What is a barn?**

Answer: 1 barn is equal to 10^{-28} m^{2} and this unit is used to measure nuclear cross-section.

**Question 4. What type of physical quantity is electric current?**

Answer: Electric current is a scalar quantity.

**Question 5. What type of physical quantity is area?**

Answer: Area is a vector quantity.

**Question 6. Give an example of the unit of a scalar quantity which is formed by two different fundamental units.**

Answer: A unit of speed is a scalar quantity which is formed by two different fundamental units.

**Question 7. Give an example of the unit of a vector quantity which is formed by two different fundamental units.**

Answer: A unit of velocity is a vector quantity which is formed by two different fundamental units.

**Question 8. What are the two present systems of the unit?**

Answer: Two present systems of the unit are:

- CGS system and
- SI.

**Question 9. Give an example of one scalar quantity and one vector quantity with the same unit.**

Answer: Speed and velocity are the two physical quantities with the same unit, speed being a scalar quantity and velocity being a vector quantity.

**Question 10. What are the fundamental units in CGS system?**

Answer: In CGS system, unit of length is a centimetre (cm), unit of mass is a gram (g) and a unit of time is a second (s).

**Question 11. In SI, how many basic units are there?**

Answer: There are seven basic units in Sl.

**Question 12. How much distance is meant by 1 AU?**

Answer: 1 AU (astronomical unit) is the average distance between the sun and the Earth.

**Question 13. Is a light year a fundamental or a derived unit?**

Answer: Light Year is a fundamental unit.

**Question 14. Which unit is used for measuring the mass of molecules and atoms?**

Answer: The unit u (unified atomic mass unit) is used for measuring the mass of molecules and atoms.

**Question 15. Which unit is used for measuring the mass of different precious stones?**

Answer: Carat is used for measuring the mass of different precious stones. 1 carat = 0.200 g.

**Question 16. What is the relationship between the Chandrasekhar limit (CSL) and the mass of the sun?**

Answer: 1 Chandrasekhar limit = 1.39 x mass of the sun.

**Question 17. Which temperature is mentioned in the definition of a litre?**

Answer: 4°C or 277 K is mentioned in the definition of a litre.

**Question 18. What is the temperature at which the density of water is maximum?**

Answer: At 4°C or 277 K, the density of water is maximum.

**Question 19. What is the density of water at 4°C?**

Answer: The density of water at 4°C is 1 g/cm^{3}.

**Question 20. Which element is mentioned in the definition of second?**

Answer: ^{133}Cs is mentioned in the definition of second.

**Question 21. Which unit is used to measure interstellar distance?**

Answer: AU (astronomical unit) is used to measure interstellar distance.

**Question 22. Is it possible to measure 0.4 mm by an ordinary scale?**

Answer: With the help of an ordinary scale, a measurement of 0.4 mm is not possible since the smallest constant in an ordinary scale is 1mm.

**Question 23. 1 gallon how many litres?**

Answer: 1 gallon 4.536 litres.

**Question 24. What is the largest unit for measurement of length?**

Answer: Parsec is the largest unit for measurement of length.

## Chapter 1 Topic A Measurement And Units Fill In The Blanks

Question 1. Specific gravity is the ratio between two quantities having the same unit. So it has ______ unit.

Answer: No

Question 2. At 4°C temperature, a volume of 1 ______of pure water is called a litre.

Answer: Kilogram, 1

Question 3. The unit of the area is a ______ unit.

Answer: Derived

Question 4. The mass of unit ______ of any material is known as the ______ of that material.

Answer: Volume, density

Question 5. The number of fundamental units in SI is ______.

Answer: 7

Question 6. The number of fundamental units in CGS system is ______.

Answer: 3

Question 7. ______ quantities have only magnitude but no direction.

Answer: Scalar

Question 8. ______ quantities have both magnitude and direction.

Answer: vector

Question 9. ______ K temperature is mentioned in the definition of litre.

Answer: 277

Question 10. ______ of water is minimum at 277 K.

Answer: Volume

Question 11. ______ is the unit of density in CGS system.

Answer: g/cm^{3}

Question 12. Parsec is a unit for measurement of ______.

Answer: Length

Question 13. Light Year is a ______ unit.

Answer: Fundamental

Question 14. ______ is the unit used for the measurement of diameters of atoms and molecules.

Answer: x-unit

Question 15. Micron is used as a unit to express dimension of ______ objects.

Answer: Microscopic

Question 16. It is convenient to express the mass of a star in terms of ______ which is a large unit of mass.

Answer: Solar mass

Question 17. 1 AU is the average distance between the ______ and the Earth.

Answer: sun

Question 18. 1 light year is equal to ______ kilometre.

Answer: 9.46 X 10^{12}

Question 19. ^{133}Cs is mentioned in the definition of ______.

Answer: Second

## Chapter 1 Topic A Measurement And Units State Whether True Or False

Question 1. Physical quantities are those natural events or phenomena which can be measured directly.

Answer: False

Question 2. Atomic mass is a unitless physical quantity.

Answer: True

Question 3. Acceleration is a vector quantity.

Answer: True

Question 4. According to CGPM, one metre is that distance which is traversed by light in air in \(\frac{1}{299702458}\)s.

Answer: False

Question 5. The unit of force is a fundamental unit.

Answer: False

Question 6. The unit of momentum is a derived unit.

Answer: True

Question 7. The density of water at 4°C is minimum.

Answer: False

Question 8. Pressure is a scalar quantity.

Answer: True

Question 9. The thickness of a plastic carry bag is measured in micron units.

Answer: True

Question 10. The fundamental units depend on each other.

Answer: False

## Chapter 1 Topic A Measurement And Units Numerical Examples

**Useful Formula**

If V be the volume of a body of mass m, the density of the body will be

If V be the volume of a sphere of radius r, then V = 4/3πr^{3}

If two liquids of density D_{1} and D_{2} are mixed in the same proportion of mass, then the density of the mixture,

**Question 1. if the density of mercury is 13.6g/cm3 In CGS, what is the density of mercury in SI?**

**Answer:**

The density of mercury in CGS, d= 13.6g/cm^{3
}

Again, 1g/cm^{3} 100kg/m^{3
}

∴ The density of mercury in SI

= 13.6 x 100kg/m^{3} = 13600 kg/m^{3}

**Question 2. If the density of iron in St is 7800 kg/m3, what is its density in CGS?**

**Answer:**

The density of iron in Sl, d= 7800 kg/m^{3
}

Again, 1 kg/m^{3} = \(\frac{1}{1000}\) g/cm^{3
}

∴ The density of iron in CGS

= 7800 ×\(\frac{1}{1000}\) g/cm^{3} = 7.8 g/cm^{3} 1000

**Question 3. The length, breadth and height of a water tank are 1.2 m, 1 m and 0.8 m, respectively. What is the volume of water contained in the tank?**

**Answer:**

Volume of water in the tank

= 1.2 m x 1m x 0.8 m

= 0.96 m^{3} = 0.96 x 1000 L = 960 L

**Question 4. If the density of a liquid is 0.8 g/cm3, what is the mass of 200 cm3 of the liquid?**

**Answer:**

Density of liquid, d=0.8 g/cm^{3
}

= Volume, V = 200 cm^{3
}

∴ If m is the mass of the liquid, d=m/v

or, m = d x V = 0.8 g/cm^{3} x 200 cm^{3} = 160 g

**Question 5. The diameter of a solid sphere of iron is 21 cm. If the density of iron is 7.8 g/cm3, what is its mass?**

**Answer:**

According to the question, the diameter of the sphere = 21 cm

∴ The radius of the sphere, r = 21/2 cm

Density of iron, d = 7.8 g/cm^{3}

∴ The volume of the sphere,

∴ Mass of the iron sphere,

m = dxV = 7.8 g/cm^{3} x 4851 cm^{3}

= 37837.8 g = 37.84 kg (approx.)

**Question 6. The densities of two liquids are 1.2 g/cm3 and 1.5 g/cm3, respectively. If the liquids are mixed in the same proportion of volume, what is the density of this mixture?**

**Answer:**

Let the mixture be prepared by taking V cm3 of each liquid.

**Mass Of The First Liquid**

= Density of first liquid x volume of the liquid

= 1.2 V g

**Mass Of The Second Liquid**

= Density of second liquid x volume of the liquid

= 1.5Vg

∴ Mass of the mixture (m) = (1.2 V+1.5 V)g = 2.7 Vg;

Volume of the mixture (V1) =(V+V)cm^{3} = 2V cm^{3}

∴ Density of the mixture,

**Question 7. Densities of two liquids are 1.2 g/cm3 and 0.8 g/cm3, respectively. If the liquids are mixed in the same proportion of mass, what is the density of this mixture?**

**Answer:**

Suppose the mixture is prepared by taking mg of both the liquids.

∴ Volume of the first liquid = m/1.2 cm^{3}

Volume of the second liquid= m/0.8 cm^{3}

**Question 8. it is known that light travels in a vacuum at a fixed velocity of 9.46 x 1012km/year (approx.). The distance of a star alpha cen- tauri from the Earth is nearly 4.24 light years. When did the light emanate from the star which we see today? What is the distance of the earth from that star in a kilometre?**

**Answer:**

As per the definition of a light year, light emanated 4.24 years back from alpha centauri.

Distance of the Earth from this star

= 4.24 light year

= 4.24 years x velocity of light in vacuum

= 4.24 x 9.46 x 1012 km

= 40.1104 x 1012 km (approx.)

**Question 9. The largest diameter of the Milky Way galaxy is nearly 9.5 x 1015 m. The average diameter of the earth is 12800 km. The average minimum diameter of all the viruses that have been discovered so far is 20 nanometres. Then, which one is smaller- the Milky Way galaxy as compared to the Earth. or the earth as compared to a virus?**

**Answer:**

**Comparison Of The Diameters Of The Milky Way Galaxy And The Earth:**

**Comparison Of The Diameters Of The Earth And A Virus:**

Clearly, a virus is much smaller as compared to the earth than the Earth as compared to the Milky Way galaxy.

**Question 10. Light takes 8 min 20 s to come from the sun to the earth. Find the distance of the earth from the sun in light year unit.**

**Answer: **

1 light year 9.46 x 1012 km

speed of light in vacuum

(c) = 3 x 10^{8} m/s = 3 x 10^{5} km/s

time (t) = 8 min 20 s = (8 x 60+20) s = 500 s .

The distance of the Earth from the sun is

d = cxt=3x 10^{3} x 500 km

=1.586 x 10^{-5} lightyear