Measurements and Experimentation

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The Measurements and Experimentation is foundational, establishing the critical role of measurement in science. It begins by defining a physical quantity as the product of a numerical value and a unit. This leads to the distinction between fundamental units (like those for length, mass, and time, which are independent) and derived units (like speed or density, which are combinations of fundamental units). The chapter emphasizes the importance of the internationally accepted S.I. System (Système International d’Unités) as the standard for scientific communication, contrasting it with older systems like CGS and FPS. Furthermore, it details the necessary characteristics of a good unit, ensuring it is invariable, reproducible, and unambiguous.

A major focus of the chapter is the practical aspect of measuring length and achieving high accuracy. It introduces the concept of Least Count (LC)—the smallest value an instrument can measure. While a metre scale is used for basic measurements, the chapter delves into precision instruments: the Vernier Callipers and the Screw Gauge. Students learn the principles of these instruments, how to calculate their respective least counts, and the essential procedure for dealing with zero error (positive and negative). A correct reading must always compensate for this error. Beyond length, the chapter also addresses the measurement of time, introducing the Simple Pendulum as an experimental setup to accurately determine the Time Period of oscillation.

In essence, this chapter equips students with the skills to conduct accurate experiments. It covers the theoretical framework of units and systems, the practical methods for precise measurements using specialised instruments, and the techniques for correcting experimental errors. This understanding of measurement, accuracy, and precision is vital, as it forms the basis for all subsequent experimental work in physics.

Exercise 1 (A)

Question 1.

What is meant by measurement?

Ans: 

Measurement is the fundamental action in science where you determine the size or magnitude of a physical property (like length, mass, or time). This is done by a process of comparison: the quantity being measured (the unknown) is compared against a fixed, universally accepted reference of the same nature, which we call a unit.

The outcome of this comparison is a complete physical quantity, expressed as a product: a numerical value that indicates how many times the standard unit is contained within the quantity, multiplied by the unit itself. For instance, stating an object has a mass of 5 kilograms quantifies that mass as five times the defined standard kilogram unit. This systematic quantification provides the necessary objective data for all scientific analysis and experimentation.

Question 2.

What do you understand about the Term Unit?

Ans: 

A unit is a definite magnitude of a physical quantity, such as length or mass, that is fixed by convention or law and used as a standard of comparison for all other quantities of the same type.

In simple terms, a unit is the reference point that gives meaning to a numerical value in a measurement.

Measurement=Numerical Value×Unit

For example, if a rope is 10 meters long, the unit is the meter (m), which is the universally accepted standard for measuring length. The number 10 indicates that the rope is 10 times the length of the standard unit.

Essential Characteristics of a Standard Unit

For a unit to be useful in science and everyday life, it must possess several key characteristics, which are now largely embodied by the International System of Units (SI):

  1. Universally Accepted (Invariable): It must be the same everywhere in the world and accepted by the international community.
  2. Well-Defined: It must be defined precisely, ideally in terms of a fundamental physical constant, so that its value does not change.
  3. Reproducible: It must be possible to accurately reproduce the standard in any laboratory.
  4. Incorruptible: Its value should not change with time or with changes in physical conditions like temperature or pressure.
  5. Appropriate Size: It should be a suitable size for measuring the quantity in question (e.g., using a meter for a desk instead of a kilometer).

Importance of Units

Units are absolutely necessary because a numerical value alone is meaningless without a reference scale.

  • Clarity and Meaning: They provide context. Saying a trip took “2” is meaningless; saying it took “2 hours” is clear.
  • Consistency: They ensure that measurements are the same regardless of who performs the measurement or where it is done. This allows scientists and engineers worldwide to share, compare, and reproduce data reliably (the core of the scientific method).
  • Dimensional Analysis: In calculations, units are manipulated algebraically to verify that the final answer has the correct physical meaning (e.g., velocity must have units of length divided by time, like m/s).

Question 3.

What are the three requirements for selecting a unit of a physical quantity?

Ans: 

The three primary requirements for selecting a reliable and universally accepted unit of a physical quantity are Invariance, Unambiguous Definition, and Reproducibility.

These characteristics ensure the unit serves as a consistent standard for scientific and commercial use worldwide.

1. Invariance (Stability and Universality)

The value of the unit must not change with respect to changes in physical conditions, location, or time.

  • Stability: The unit should remain constant over a long period. For example, the definition of the second (the SI unit of time) is now based on a specific, unchanging transition of the cesium-133 atom, making it inherently stable.
  • Universality (or Invariance with Space): The unit must remain the same regardless of where the measurement is performed (on Earth, in space, or in different labs). This ensures measurements are comparable everywhere.

2. Unambiguous Definition (Clarity)

The unit must be clearly and precisely defined so that everyone can have the exact same understanding of what it represents.

  • The definition should be precise enough that it can be measured with extreme accuracy.
  • Ideally, the unit should be defined in terms of fundamental physical constants of nature (like the speed of light or the Planck constant), rather than a physical artifact that can be damaged or lost.

3. Reproducibility (Practicality)

It must be possible to reproduce the unit easily and accurately in any standard laboratory, allowing for consistent measurement and calibration.

  • This means that the standard quantity can be easily accessed or the procedure for generating the unit can be repeated to verify the measurement.
  • A unit should also be of a convenient size for practical measurements (e.g., the kilometer is used for road distances, while the millimeter is used for mechanical drawings).

Question 4.

Name the three fundamental quantities.

Ans: 

The three most commonly referenced fundamental quantities in the field of physics, particularly in classical mechanics, are:

  1. Length (Unit: meter, m)
  2. Mass (Unit: kilogram, kg)
  3. Time (Unit: second, s)

These three quantities are considered the basic building blocks from which all other mechanical quantities (like velocity, force, and energy) can be mathematically derived.

Question 5.

Name the three systems of units and state the various fundamentals units in them.

Ans: 

System of UnitsFundamental QuantityUnit NameUnit Symbol
CGS SystemCentimeterCentimetercm
GramGramg
SecondSeconds
\hline
MKS SystemMeterMeterm
KilogramKilogramkg
SecondSeconds
\hline
FPS SystemFootFootft
PoundPound (for mass)lb
SecondSeconds

Question 6.

Define a fundamental unit.

Ans:

A fundamental unit (or base unit) is a standard unit of measurement for a basic physical quantity that is:

  1. Independent: It is defined on its own and does not rely on any other units for its definition.
  2. Basic: It cannot be broken down into simpler units.
  3. Foundation: All other units of measure (derived units) are created by algebraically combining these fundamental units.

In the globally accepted International System of Units (SI), there are seven fundamental units that form the basis for all scientific measurements.

The Seven SI Fundamental Units

Base QuantityFundamental UnitSymbol
LengthMeterm
MassKilogramkg
TimeSeconds
Electric CurrentAmpereA
Thermodynamic TemperatureKelvinK
Amount of SubstanceMolemol
Luminous IntensityCandelacd

Key Characteristics

  • Non-Derivable: You cannot express a fundamental unit (like the meter) as a combination of other fundamental units (like the second and kilogram).
  • Universal Definition: Their definitions are based on invariant physical constants or phenomena (e.g., the speed of light) to ensure they are the same everywhere.
  • Building Blocks: Units for complex quantities like velocity (meter/second) or force (Newton, which is kg⋅m/s2) are derived from these fundamental units.

Question 7.

What are the fundamental units in the S.I system? Name them along with their symbols.

Ans: 

The fundamental units of measurement in the International System of Units (SI) are the seven Base Units. These units are independent of each other and form the foundation from which all other SI units (derived units) are created.

7 Fundamental SI Units (Base Units)

Base QuantitySI Unit (Name)SI Unit (Symbol)
Lengthmetre (or meter)m
Masskilogramkg
Timeseconds
Electric CurrentampereA
Thermodynamic TemperaturekelvinK
Amount of Substancemolemol
Luminous Intensitycandelacd

What are Fundamental Units?

Fundamental (or Base) Units are the set of seven basic units that are not defined in terms of any other units. They are the essential building blocks for measuring physical quantities. For example, the unit for force, the Newton (N), is a derived unit because it is defined using three fundamental units: N=kg⋅m/s2.

Question 8.

Explain the meaning of the derived unit with the help of one example?

Ans: 

A derived unit is a unit of measurement created by mathematically combining two or more fundamental (base) units. These units are used to quantify physical quantities whose definitions rely on formulas involving the base quantities. While fundamental units (such as the meter, kilogram, or second) stand on their own, derived units are built upon them using multiplication, division, or exponents.

For instance, consider the unit for Speed. Speed is defined by the formula Distance/Time. By replacing these quantities with their respective fundamental SI units, we derive the unit for speed:

Unit of Speed=Unit of Time /Unit of Distance​=second (s)meter (m)​=m/s

The m/s (meters per second) is therefore a derived unit. Similarly, the unit for Force, the Newton (N), is derived from the units of mass, length, and time: N=kg⋅m/s2. The concept of derived units allows the entire system of physical measurement to be consistently and coherently linked back to a small set of defined base units.

Question 9.

Define Standard metre.

Ans: 

The modern definition of the metre (m), the SI base unit for length, is tied to a fundamental constant of nature to guarantee extreme precision and universality. The Standard Metre is currently defined as:

This definition is unique and highly stable for the following key reasons:

  1. Fixed Speed of Light: It effectively fixes the numerical value of the speed of light (c) at exactly 299,792,458 meters per second (m/s). The metre is thus not defined by a physical object (like an old metal bar) but by this universal constant.
  2. Universal Reproducibility: Since the speed of light is constant everywhere, the definition ensures that the standard for the metre is universally available and highly reproducible with high accuracy.
  3. Dependence on Time: The accuracy of the metre is now inherently linked to the accuracy of the SI base unit for time, the second. The second is itself defined using another unchanging atomic constant (the frequency of the cesium-133 atom).

Question 10.

Name two units of length which are bigger than a metre. How are they related to the metre?

Ans:

Two units of length that are significantly bigger than a metre are the Kilometre and the Astronomical Unit.

  1. Kilometre (km):
    • The kilometre is the standard unit used for measuring large terrestrial distances, such as the distance between cities or the length of a road.
    • Relation to the Metre: A kilometre is equal to one thousand metres.

      1 km=1000 m
  2. Astronomical Unit (AU):
    • The Astronomical Unit is a unit of distance used primarily for measuring distances within our solar system. It is defined as the average distance between the Earth and the Sun.
    • Relation to the Metre: One Astronomical Unit is approximately equal to 149.6 billion metres.

      1 AU≈1.496×1011 m

Question 11.

Write the names of two units of length smaller than a metre. Express their relationship with the metre.

Ans:

Two units of length smaller than a metre and their relationship with the metre are:

  1. Centimetre (cm): One metre contains one hundred centimetres.
    1 cm=10−2 mor1 m=100 cm
  2. Millimetre (mm): One metre contains one thousand millimetres.
    1 mm=10−3 mor1 m=1000 mm

Note: Other commonly used units smaller than a metre include the micrometre (μm) and the nanometre (nm).

Question 12.

How is nanometer related to Angstrom?

Ans:

The nanometer (nm) and the Angstrom (A˚) are both metric units of length used to measure extremely small distances, such as atomic dimensions and wavelengths of light. The relationship between them is straightforward: one nanometer is equal to ten Angstroms.

The conversion factors based on the standard unit, the meter (m), are:

  • 1 nanometer (nm)=10−9 m
  • 1 Angstrom (A˚)=10−10 m

Therefore, mathematically:

1 nm=10−10 m/A˚10−9 m​=10(−9)−(−10) A˚=101 A˚

This means the Angstrom is a smaller unit than the nanometer. While the nanometer is an official SI unit prefix, the Angstrom is a non-SI unit, though it is still commonly used in fields like crystallography and atomic physics because it conveniently expresses bond lengths and atomic radii.

Question 13.

Name the three convenient units used to measure length ranging from very short to very long value. How are they related to the S.I unit?

Ans:

The three convenient units of length used to measure values ranging from very short to very long, along with their relation to the S.I. unit (the meter, m), are:

RangeUnit Name (Symbol)Used to MeasureRelation to S.I. Unit (Meter, m)
Very ShortAngstrom (A˚)Atomic sizes, chemical bond lengths, and wavelengths of X-rays.1 A˚=10−10 m
IntermediateCentimeter (cm)Everyday objects like the length of a pencil or a person’s height.1 cm=10−2 m
Very LongLight Year (ly)Interstellar and astronomical distances (e.g., distance to stars).1 ly≈9.46×1015 m

Relation to the S.I. Unit

The S.I. unit of length is the meter (m). All other units of length are defined in terms of the meter, either as decimal multiples/submultiples (using S.I. prefixes) or as separate non-S.I. units with a defined conversion factor.

  1. Angstrom (A˚): This unit is a non-S.I. unit used for extremely small measurements. It is defined as exactly one ten-billionth of a meter.
    1 Angstrom=1×10−10 m
  2. Centimeter (cm): This is a decimal submultiple of the S.I. unit, where the prefix centi- means one hundredth (10−2).
    1 Centimeter=1×10−2 m
  3. Light Year (ly): This is a non-S.I. unit used for astronomical distances. It is defined as the distance light travels in a vacuum in one Julian year. When converted, its value is an extremely large multiple of the meter.

    1 Light Year≈9,460,730,472,580,800 m
    or 1 ly≈9.46×1015 m

Question 14.

Name the S.I unit of mass and define it.

Ans:

The kilogram (kg), the S.I. unit of mass, is now defined by fixing the exact numerical value of the Planck constant (h).

This modern definition sets the value of h as precisely 6.62607015×10−34 when expressed in the unit J⋅s (joule-second), which is equivalent to kg⋅m2⋅s−1. Because the values for the meter (m) and the second (s) are already established using other fundamental constants, the kilogram’s value is derived from this fixed constant. This connection is physically realized using a highly sophisticated weighing apparatus known as the Kibble balance . By basing the kilogram on a universal constant of nature, the standard is now universally stable and reproducible, overcoming the historical issue of relying on a fragile physical object (the International Prototype of the Kilogram) whose mass could change over time.

Question 15.

(a) Complete the following: 1 light year =……….m

(b) Complete the following: 1 m =……….Å

(c) Complete the following: 1 m  =……….. µ

(d) Complete the following: 1 micron =………..Å

(e) Complete the following: 1 fermi = ……….. M

Ans:

(a) 1 light year = 9.46×1015

(b) 1 m = 1010 A˚ (Angstrom) 

(c) 1 m = 106 μ (micron)

(d) 1 micron (μ) = 104 A˚ (Angstrom) 

(e) 1 fermi (f) = 10−15 m

Question 16. 

State two units of mass smaller than a kilogram. How are they related to kilogram?

Ans:

Two units of mass that are smaller than a kilogram (kg) are the gram (g) and the milligram (mg).

Relation to Kilogram

  1. Gram (g): The gram is one thousandth of a kilogram. This is based on the metric prefix ‘kilo’ which means 1000. The relationship is:
    1 gram=10001​ kilogramor1 g=10−3 kg
  2. Milligram (mg): The milligram is one millionth of a kilogram. It is also one thousandth of a gram (the prefix ‘milli’ means 10−3). The relationship is:
    1 milligram=1,000,0001​ kilogramor1 mg=10−6 kg

Question 17. 

State two units of mass bigger than a kilogram. Give their relationship with the kilogram?

Ans:

Two units of mass larger than a kilogram (kg) are the Quintal and the Metric Tonne.

Here is their relationship with the kilogram:

  1. Quintal (q)
    • Relationship: One quintal is equivalent to 100 kilograms.
    • Formula: 1 q=100 kg
  2. Metric Tonne (t)
    • Relationship: One metric tonne is equivalent to 1000 kilograms.
    • Formula: 1 t=1000 kg

The Metric Tonne is often used to measure the mass of large, bulk commodities in trade and industry, such as grains, metals, or vehicle cargo.

Question 18. 

(a)Complete the following: 1 g =………kg 

(b) Complete the following : 1 mg =………kg 

(c) Complete the following: 1 quintal =………kg 

(d)Complete the following : 1 a.m.u (or u) =……..kg

Ans:

UnitConversion to Kilogram (kg)
(a) 1 g10−3 kg
(b) 1 mg10−6 kg
(c) 1 quintal100 kg
(d) 1 a.m.u (or u)1.6605×10−27 kg

Question 19. 

Name the S.I unit of time and define it.

Ans:

The modern definition of the second (s), the S.I. unit of time, is based on a fundamental and unchanging atomic property, which ensures its exceptional accuracy and universal consistency.

One second is formally defined as the duration of exactly 9,192,631,770 periods of the radiation produced by the transition between the two specific hyperfine energy levels of an unperturbed Caesium-133 atom in its ground state. This definition effectively fixes the numerical value of the Caesium-133 transition frequency (ΔνCs​) at 9,192,631,770 Hertz (Hz), where Hz is equivalent to s−1. By referencing a constant of nature—the resonant frequency of the Caesium-133 atom—the second is made the most stable and accurately measurable of all the fundamental S.I. units.

Question 20.

Name two units of time bigger than a second. How are they related to the Second?

Ans:

Two units of time that are bigger than a second (s) are the minute (min) and the hour (h).

Their relationship to the second, which is the SI base unit of time, is as follows:

  1. Minute (min):
    • One minute is defined as a duration of 60 seconds.
    • Relation to Second: 1 min=60 s
  2. Hour (h):
    • One hour is defined as a duration of 60 minutes.
    • Since 1 minute is 60 seconds, one hour is equal to 60×60=3600 seconds.
    • Relation to Second: 1 h=3600 s

Question 21. 

What is a leap year?

Ans:

A leap year is a calendar year that contains an extra day, making it 366 days long instead of the usual 365. This additional day, known as a leap day, is added to the month of February, extending it to February 29th. The purpose of a leap year is to keep our civil calendar synchronized with the solar year (the actual time it takes the Earth to complete one full orbit around the Sun).

The Earth’s orbit takes approximately 365.2422 days (or about 365 days and 6 hours). If we only used a 365-day year, we’d lose roughly six hours every year. Over a century, the calendar would drift by about 24 days, causing seasons to gradually fall out of alignment with the calendar dates. By adding a leap day almost every four years, we largely correct this accumulated discrepancy, ensuring that the seasons begin consistently around the same time each year.

The rules for determining a leap year under the Gregorian calendar (the one used by most of the world) are:

  1. A year is a leap year if it is evenly divisible by 4 (e.g., 2024, 2028).
  2. Exception 1: If the year is evenly divisible by 100, it is not a leap year (e.g., 1700, 1800, 1900).
  3. Exception 2: If the year is evenly divisible by 400, it is a leap year (e.g., 1600, 2000, 2400).

This set of rules results in an average year length of 365.2425 days, which is extremely close to the true solar year, keeping the calendar accurate for centuries.

Question 22.

The year 2020 will have February of 29 days’. Is this statement true?

Ans:

The statement, “The year 2020 will have February of 29 days,” is True

Explanation

The year 2020 was a Leap Year, which means it had 366 days instead of the usual 365. This extra day is added to the calendar by extending the month of February from 28 days to 29 days.

The rules of the Gregorian calendar determine a leap year:

  1. A year is typically a leap year if it is evenly divisible by 4 (which 2020÷4=505, a whole number).
  2. Exception 1: Years divisible by 100 (like 1900 or 2100) are not leap years…
  3. Exception 2:unless they are also divisible by 400 (like 2000 or 2400), in which case they are leap years.

Since 2020 is divisible by 4 but not by 100, it satisfied the primary rule for a leap year, confirming that its February contained the extra day, February 29th.

Question 23.

What is a lunar month?

Ans:

A lunar month is a unit of time that is based on the Moon’s motion and its cycle of phases.

The most common and practical definition of a lunar month is the synodic month (or lunation), which is the average time it takes for the Moon to complete one cycle of its visible phases—for example, from one New Moon to the next.

Key Facts about the Lunar Month (Synodic Month)

  • Duration: The average length of a synodic month is approximately 29.53 days (specifically, 29 days, 12 hours, 44 minutes, and 3 seconds).
  • Basis: This duration is determined by the alignment of the Moon, Earth, and Sun. Because the Earth is constantly orbiting the Sun, the Moon has to travel an extra distance in its orbit after completing a full revolution around the Earth to “catch up” and return to the same alignment (i.e., the same phase, like New Moon).
  • Calendars: Lunar calendars (like the Islamic Hijri calendar) and lunisolar calendars (like the Chinese and Jewish calendars) base their months on this cycle, typically alternating between 29 and 30 days to closely match the average 29.5 days.

Other Astronomical Lunar Months

In astronomy, there are several other precise definitions of a “month” based on different reference points:

  • Sidereal Month: The time it takes for the Moon to complete one full orbit around the Earth when measured against the background of fixed stars. This is shorter than the synodic month, lasting about 27.32 days.
  • Anomalistic Month: The time it takes for the Moon to return to its closest point to Earth (perigee). This cycle is important for determining the size and intensity of tides and phenomena like a Supermoon, lasting about 27.55 days.
  • Draconic Month: The time it takes for the Moon to pass through the same orbital node (the points where the Moon’s orbit crosses the Earth’s orbital plane). This period is crucial for predicting eclipses and lasts about 27.21 days.

Question 24. 

(a) Complete the following: 1 nano second =……….s.

(b) Complete the following: 1 µs =……….s 

(c) Complete the following: 1 mean solar day = _______ s.

(d) Complete the following: 1 year =……….s.

Ans:

ConversionValue in Seconds (s)
(a) 1 nano second (ns)10−9 s
(b) 1 microsecond (μs)10−6 s
(c) 1 mean solar day86,400 s
(d) 1 year (≈365 days)31,536,000 s (≈3.15×107 s)

Question 25. 

(a) Name the physical quantities which are measured in the given units:- u 

(b) Name the physical quantities which are measured in the given units:- ly 

(c) the physical quantities which are measured in the given units:- ns

(d) Name the physical quantities which are measured in the given units:- nm

Ans: 

UnitPhysical Quantity Measured
(a) u (or amu)Mass (specifically, atomic/molecular mass)
(b) ly (Light Year)Length or Distance (specifically, astronomical distances)
(c) ns (nanosecond)Time
(d) nm (nanometer)Length

Question 26. 

(a) Write the derived unit of speed

(b) Write the derived unit of force

(c) Write the derived unit of work

(d) Write the derived unit of the pressure

Ans:

The derived units in the International System of Units (SI) for the given quantities are:

QuantityDerived Unit (Special Name)Derived Unit (in Base Units)
(a) SpeedNone (N/A)metre per second (m/s or m⋅s−1)
(b) ForceNewton (N)kilogram metre per second squared (kg⋅m/s2 or kg⋅m⋅s−2)
(c) WorkJoule (J)kilogram metre squared per second squared (kg⋅m2/s2 or N⋅m)
(d) PressurePascal (Pa)kilogram per metre per second squared (kg/(m⋅s2) or N/m2)

Explanation

Derived units are defined by multiplying or dividing SI base units (like metre, kilogram, second) according to the physical formula:

  • Speed: Speed=Distance/Time. The unit is metre/second.
  • Force: Force=Mass×Acceleration. Since Acceleration is m/s2, the unit is kg⋅m/s2, which is named the Newton (N).
  • Work: Work=Force×Distance. The unit is Newton×metre (N⋅m), which is named the Joule (J).
  • Pressure: Pressure=Force/Area. The unit is Newton/metre2 (N/m2), which is named the Pascal (Pa).

Question  27.

(a) How are the following derived units related to the fundamental unit?

Newton

(b) How are the following derived units related to the fundamental unit?

watt

(c) How are the following derived units related to the fundamental unit?

joule

(d) How are the following derived units related to the fundamental unit?

Pascal

Ans: 

Derived UnitQuantityRelationship to Fundamental UnitsFormula Basis
(a) Newton (N)Forcekg⋅m⋅s−2Force=mass×acceleration
(b) Watt (W)Powerkg⋅m2⋅s−3Power=timework​
(c) Joule (J)Energy or Workkg⋅m2⋅s−2Work=force×distance
(d) Pascal (Pa)Pressurekg⋅m−1⋅s−2Pressure=areaforce​

Question  28. 

(a) Name the physical quantity related to the following unit :- km2

(b) Name the physical quantity related to the following unit:-Newton

(c) Name the physical quantity related to the following unit :- Joule

(d) Name the physical quantity related to the following unit: Pascal

(e) Name the physical quantity related to the following unit:- watt

Ans:

(a) km2 is the unit for Area (km2 stands for square kilometre). 

(b) Newton (N) is the unit for Force.

(c) Joule (J) is the unit for Energy or Work

(d) Pascal (Pa) is the unit for Pressure

(e) Watt (W) is the unit for Power.

Exercise 1 (A)

Question 1. 

The fundamental unit is:-

  1. Newton
  2. Pascal
  3. hertz
  4. second

Question 2.

Which of the following unit is not a fundamental unit:

  1. metre
  2. Litre
  3. second
  4. kilogram

Question 3.

The unit of time is :

  1. light year
  2. parsec
  3. leap year
  4. angstrom

Question 4.

1 Å is equal to :

  1. 0.1 nm
  2. 10-10 cm
  3. 10-8 m
  4. 104 µ

Question 5.

ly is the unit of:-

  1. time
  2. length
  3. mass
  4. none of this