PHYSICS

Chapter 1: Measurements and Experimentation

Syllabus: (i) International System of Units, the required SI units with correct symbols. Other commonly

used system of units - fps and cgs.

(ii) Measurements using common instruments, Vernier callipers and micro-metre screw gauge for

length, and simple pendulum for time.

Measurement of length using, Vernier callipers and micro-metre screw gauge.

Decreasing least-count leads to an increase in accuracy;

least-count (LC) of Vernier callipers and screw gauge), zero error (basic idea), (no

numerical problems on callipers and screw gauge),

Simple pendulum; time period, frequency, graph of length l vs. T2 only.

Slope of the graph. Formula T=2π√𝑙

𝑔 (only simple numerical problems.)

TOPIC-1 – INTRODUCTION AND INTERNATIONAL SYSTEM OF UNITS Click the link below to have a better understanding to the introduction of the topic.

https://youtu.be/oAtDAoqdExw

In this topic, you will learn some important definitions and terms related to measurement, fundamental and derived

units, and some units of measure.

Measurement: Measurement is the process of comparison of the given physical quantity with the known standard

quantity of the same nature.

Unit: Unit is the quantity of a constant magnitude which is used to measure the magnitudes of other quantities of

the same nature.

Fundamental or Basic Units:

A fundamental or basic unit is that which is independent of any other unit or which can neither be changed nor can

be related to any other unit.

The units of mass, length, time, temperature, current and amount of substance are fundamental units.

Derived Units:

Derived units are those which depend on the fundamental units or which can be expressed in terms of the

fundamental units.

For example, for the measurement of area, we need a unit which is length x length or (length) 2

A NOTE ON SI UNITS SI units (Systeme International d’Unites) were adopted internationally in 1968.

OTHER COMMONLY USED SYSTEM OF UNITS - FPS AND CGS.

CGS system: The full form of CGS system is Centimeter Gram Second system. In this system, the fundamental units

are Centimeter, Gram, Second.

FPS system: The full form of FPS system is Foot Pound Second system. In this system, the fundamental units are

Foot, Pound, Second.

TOPIC-2 – MEASUREMENT OF LENGTH In this topic, you will learn about measuring devices like Vernier callipers, micro-metre screw gauge and how to use

them.

For Vernier calliper: https://youtu.be/T2HMf2d9fkE

Vernier Callipers:

Pierre Vernier invented the Vernier Calliper. Distances smaller than millimetres cannot be measured by using regular

measuring scales whereas a device like the Vernier Calliper can measure extremely small distances.

Principle of Vernier:

Using this method, you can measure lengths up to the 2nd decimal place of a centimetre that is values of 0.1 mm or

0.01 cm can be measured correctly.

This technique uses two scales:

The fixed scale otherwise called the main scale.

The other scale called the Vernier scale slides along the main scale.

Least Count (L.C.) of Vernier is also called the Vernier Constant.

L.C. = Value of 1 main scale division – Value of 1 Vernier scale division

Description of Vernier:

The outside jaws are used to measure the length of a rod, the diameter of a sphere or external diameter of a

cylinder.

The inside jaws are used to measure the internal diameter of a hollow cylinder or pipe.

The strip T is used to measure the depth of a small beaker or bottle.

The main scale helps to measure length correctly up to 1 mm.

Vernier scale helps to measure length correctly up to 0.1 mm.

Least Count of Vernier Callipers:

L.C. = Value of 1 main scale division / Total number of divisions on Vernier scale

Positive Zero Error:

On bringing both the jaws together, if the zero mark of the Vernier scale is on the right of the zero mark of the main

scale, the zero error is said to be positive.

Zero error = the number of Vernier division which coincides with any division of the main scale x L.C.

The value of this error is always positive.

Negative Zero Error:

On bringing both the jaws together, if the zero mark of the Vernier scale is on the left of the zero mark of the main

scale, the zero error is said to be negative.

Zero error = (the number of Vernier division which coincides with any division of the main scale – the total number

of Vernier divisions) x L.C.

The value of this error is always negative.

Measurement of length of an object using Vernier callipers:

Observed length

= Main scale reading + (Vernier division p coinciding with any division on the main scale) x L.C.

True or correct length = Observed length – Zero error (with sign)

Screw Gauge:

For Screw gauge: https://youtu.be/zv4jT-A8RKw

A screw gauge is an instrument used for measuring the diameter of a thin wire or the thickness of a sheet of

metal. It consists of a U-shaped frame fitted with a screwed spindle which is attached to a thimble.

Principle of Screw gauge:

It works on principle of screw.

The pitch of a screw is the distance moved by the screw along its axis in one complete rotation of its head.

Generally, the pitch of a screw is 1 mm or 0.5 mm.

Least Count of a Screw Gauge:

L.C. = Pitch of screw gauge/ Total number of divisions on its circular scale

Pitch of screw gauge is the linear distance moved by its screw on the main scale when the circular scale is given one

complete revolution

Description of screw gauge:

The ratchet is used to advance the screw by turning it till the object is gently held between the stud and

spindle of the screw.

The sleeve is used to mark main scale and baseline.

The thimble is used to mark circular scale.

The main scale helps to measure length correct up to 1 mm.

The circular scale helps to measure length correct up to 0.01 mm.

ZERO ERROR IN SCREW GAUGE:

Positive Zero Error:

On bringing both the spindle and the stud together, if the zero mark of the circular scale is below the

baseline of the main scale, the zero error is said to be positive.

Zero error = the number of circular scale division which coincides with the baseline x L.C.

The value of this error is always positive.

Negative Zero Error:

On bringing both the spindle and stud together, if the zero mark of the circular scale is above the baseline of

the main scale, the zero error is said to be negative.

Zero error = (The number of circular scale division which coincides with the baseline – The total number of

circular scale divisions) x L.C.

The value of this error is always negative.

Backlash Error:

This error is caused due to the wear and tear of threads of the screw.

It is observed that on reversing the direction of rotation of the thimble, the tip of the screw does not start

moving in the opposite direction at once, but it remains stationary for a part of rotation.

To avoid this error, the screw should be rotated in one direction only while taking the measurements.

TOPIC-3 – MEASUREMENT OF TIME

For Simple Pendulum: https://youtu.be/p1Mkac41_qo

In this topic, you will learn about the measurement of time.

Time is measured as the gap between two events irrespective of the duration of the event.

Instruments used to measure time:

Simple Pendulum: A simple pendulum is a heavy point mass (called the bob) suspended from a rigid support

by a massless and inextensible string.

Compound Pendulum: This is capable of oscillating about the horizontal axis passing through it.

Seconds Pendulum: The time period of oscillation is equal to two seconds.

SIMPLE PENDULUM:

The oscillatory motion of a simple pendulum: Oscillatory motion is defined as the to and fro motion of the

pendulum in a periodic fashion and the centre point of oscillation known as equilibrium position.

The time period of a simple pendulum: It is defined as the time taken by the pendulum to finish one full

oscillation and is denoted by “T”.

The amplitude of simple pendulum: It is defined as the distance travelled by the pendulum from the

equilibrium position to one side.

Length of a simple pendulum: It is defined as the distance between the points of suspension to the centre of

the bob and is denoted by “l”.

Frequency of simple pendulum: No of oscillations made in one second.

Graph showing the variation of square of time period (T2) with the length (l) of a pendulum:

Measurement of time period using a simple pendulum:

The time period of oscillation (T) is:

Directly proportional to the square root of its effective length. i.e. T∝√l

Inversely proportional to the square root of acceleration due to gravity (g). i.e. T∝ 1/√g

The time period of oscillation (T) does not depend on:

The mass or material of the body suspended i.e., the bob.

The extent of swing on either side (i.e., the amplitude).

WORKSHEET

Question 1

What is meant by measurement?

Answer 1

Measurement is the process of comparing a given physical quantity with a known standard quantity of the

same nature.

Question 2

What do you understand by the term unit?

Answer 2

Unit is a quantity of constant magnitude which is used to measure the magnitudes of other quantities of

the same manner.

Question 3

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

Answer 3

The three requirements for selecting a unit of a physical quantity are

(i) It should be possible to define the unit without ambiguity.

(ii) The unit should be reproducible.

(iii) The value of units should not change with space and time.

Question 4

Define the three fundamental quantities.

Answer 4

S.I. unit of length (m): A metre was originally defined in 1889 as the distance between two marks drawn

on a platinum-iridium (an alloy made of 90% platinum and 10% iridium) rod kept at 0°C in the

International Bureau of Weights and Measures at serves near Paris.

S.I. unit of mass (kg): In 1889, one kilogramme was defined as the mass of a cylindrical piece of a

platinum-iridium alloy kept at International Bureau of Weights and Measures at serves near Paris.

S.I. unit of time (s): A second is defined as 1/86400th part of a mean solar day, i.e.

1 s = 1/86400 × one mean solar day.

Name the three systems of unit and state their various fundamental units.

Answer 5

Three systems of unit and their fundamental units:

(i) C.G.S. system (or French system): In this system, the unit of length is centimeter (cm), unit of mass is

gram (g) and unit of time is second (s).

(ii) F.P.S. system (or British system): In this system, the unit of length is foot (ft), unit of mass is pound

(lb) and unit of time is second (s).

(iii) M.K.S. system (or metric system): In this system, the unit of length is meter (m), unit of mass is

kilogramme (kg) and unit of time is second (s).

Question 6

Define a fundamental unit.

Answer 6

A fundamental (or basic) unit is that which is independent of any other unit or which can neither be

changed nor can be related to any other fundamental unit.

Question 7

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

Answer 7

Fundamental quantities, units and symbols in S.I. system are

Quantity Unit Symbol

Length metre m

Mass kilogramme kg

Time second s

Temperature kelvin K

Luminous intensity candela cd

Electric current ampere A

Amount of substance mole mol

Angle radian rd

Solid angle steradian st-rd

Question 8

Explain the meaning of the term ‘least count of an instrument’ by taking a suitable example.

Answer 8

The least count of an instrument is the smallest measurement that can be taken accurately with it. For

example, if an ammeter has 5 divisions between the marks 0 and 1A, then its least count is 1/5 = 0.2 A or

it can measure current up to the value 0.2 accurately.

Question 9

A boy makes a scale with graduations in cm on it, i.e. 100 divisions in 1 m. To what accuracy can this

scale measure? How can this accuracy be increased?

Answer 9

Total length of the scale = 1 m = 100 cm

No. of divisions = 100

Length of each division = Total length/total no. of divisions

= 100 cm/100

= 1 cm

Thus, this scale can measure with an accuracy of 1 cm.

To increase the accuracy, the total number of divisions on the scale must be increased.

Question 10

A boy measures the length of a pencil by a metre rule and expresses it to be 2.6 cm. What is the least count

of the metre rule? Can he write it as 2.60 cm?

Answer 10

The least count of a metre rule is 1 cm.

The length cannot be expressed as 2.60 cm because a metre scale measures length correctly only up to one

decimal place of a centimetre.

Question 11

Define the least count of Vernier callipers. How do you determine it?

Answer 11

The least count of Vernier callipers is equal to the difference between the values of one main scale division

and one vernier scale division.

Let n divisions on vernier callipers be of length equal to that of (n – 1) divisions on the main scale and the

value of 1 main scale division be x. Then Value of n divisions on vernier = (n – 1) x

Alternatively, value of 1 division on vernier = (n – 1) x / n

Hence,

Least count:

L.C. = (Value of one main scale division) / (Total no. of divisions on vernier callipers)

Value of one main scale division = 1 mm

Total no. of divisions on Vernier = 10

Therefore, L.C. =1/10 cm=.1 cm=1mm

Question 12

Define the term ‘Vernier constant’.

Answer 12

Vernier constant is equal to the difference between the values of one main scale division and one vernier

scale division. It is the least count of vernier callipers.

Question 13

When is a vernier calipers said to be free from zero error?

Answer 13

A vernier calipers is said to be free from zero error, if the zero mark of the vernier scale coincides with

the zero mark of the main scale.

Question 14

State three uses of the vernier callipers.

Answer 14

Three uses of vernier callipers are

(a) Measuring the internal diameter of a tube or a cylinder.

(b) Measuring the length of an object.

(c) Measuring the depth of a beaker or a bottle.

Question 15

State the purpose of ratchet in a screw gauge.

Answer 15

Ratchet helps to advance the screw by turning it until the object is gently held between the stud and spindle

of the screw.

Question 16

A stopwatch has 10 divisions graduated between the 0 and 5 s marks. What is its least count?

Answer 16

Range of the stop watch = 5s

Total number of divisions = 10

L.C. = 5/10 = 0.5 s

Question 17

Define the terms: (i) oscillation, (ii) amplitude, (iii) frequency and (iv) time period as related to a simple

pendulum.

Answer 17

(i) Oscillation: One complete to and fro motion of the pendulum is called one oscillation.

(ii) Amplitude: The maximum displacement of the bob from its mean position on either side is called the

amplitude of oscillation. It is measured in metres (m).

(iii) Frequency: It is the number of oscillations made in one second. Its unit is hertz (Hz).

(iv) Time period: This is the time taken to complete one oscillation. It is measured in second (s).

Question 18

A simple pendulum completes 40 oscillations in a minute.

Find its (a) Frequency and (b) Time period.

Answer 18

(a) Frequency = Oscillations per second

= (40/60) s-1

= 0.67 s-1

(b) Time period = 1/frequency

= (1/0.67) s

= 1.5 s

Question 19

The time period of a simple pendulum is 2 s. What is its frequency? What name is given to such a

pendulum?

Answer 19

Time period = 2 s

Frequency = 1/time period

= (½) s-1

= 0.5 s-1

Such a pendulum is called the seconds’ pendulum.

Question 20

How much time does the bob of a second’s pendulum take to move from one extreme to the other extreme

of its oscillation?

Answer 20

Time period of a seconds’ pendulum = 2 s

Time taken to complete half oscillation, i.e. from one extreme to the other extreme = 1 s.