We learn many things by careful observations of phenomena of nature. The ultimate test of physical theory is
its agreement with observations and measurement of physical phenomena.
Physics is basically a science of measurements.
According to LORD KELVIN (1824-1907), one of the greatest scientists, unless you can measure what you are speaking about and express it in numbers you have not started exact science.
For the measurement of any physical quantity we choose a constant quantity as a standard. We compare this standard quantity with the given physical quantity to find the number, which express how many times a standard quantity is contained in a physical quantity.
The standard quantity (Constant quantity), used for comparison, is called unit.
MEASUREMENT is the comparison of an unknown quantity with a known standard quantity (Constant Quantity) or unit.
In order to express the result of measurement, we must know:
i) The unit in which a quantity is measured
ii) The numerical value which express how many times a standard quantity or unit is contained in a given physical quantity.
Example: If we have to measure weight of a book, we use standard weighing (kg) machine. ON measurement, if we find that 5 times the standard weight, then the weight is 5 kg. In the above statement 5 is the unit of physical quantity.
Magnitude of a Physical Quantity: The number of times a standard quantity is present in a given physical quantity is called magnitude of physical quantity.
Physical quantity = (Magnitude) × (Unit)
Need for the introduction of standard Quantity: From ancient times, man has been facing the necessity of measuring and estimating various quantities. For measuring mass, he used various kinds of standards. For measuring length, he used foot length or arm length etc. However, pants of human body differ in lengths for different people. This lead to a lot of confusion.
However, with development in science, same standards of measurement adopted world wide. This led to avoid all kinds of confusion.
The first serious attempt to standardise the units was made in 1889 in paris. However some anomalies were left. In october 1960, another conference was held and the standard units were revised.
Characteristics of Standard Unit:
i. It should be of convenient size
ii. It should be easily reproduced
iii. It should not be change with respect to space and time.
iv. It should be possible to define, without any doubt or ambiguity.
v. It should not be perishable.
Fundamental Units:
The Units, which can neither be derived from one another, nor can they be resolved
(broken) in to anything more basic are called fundamental units.
Examples of fundamental units: Mass (M), Length (L), Time (T), Temperature, Luminous
intensity, Electric charge and Electric current are fundamental units.
The Matric System: In 1789 a system of measurement was inverted upon the powers
often. This was logical. Once the size of the unit had been determined say, the ''metre'',
submultiples were named decimetre, centimetre, millimetre for one tenth, one hundredth etc
of a metre respectively, multiples are named as the decametre (× 10) hectametre (× 100),
kilometre (× 1000) etc. This system is called metric system which literally means "measuring
system". This further classified as M.K.S. and C.G.S. system.
In 1968, a single system of units had been established internationally. This is known as international system of units. (S.I.)
The following table shows the basic units in the S.I. system together with their symbols:
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Basic Units Of S.I System
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Physical Quantity
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Name of the unit
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Symbol
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Length
Mass
Time
Temparature
Electric Current
Luminious Intensity
Amount Of Substance
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Metre
Kilogram
Second
Kelvin
Ampere
Candela
mole
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M
Kg
S
K
A
Cd
mol
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Derived Units: Any units which can be obtained by the combination of one or more fundamental units, is called derived units.
In mechanics, derived units can be obtained from fundamental units of man, length and time
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Physical Quantity
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Delivered Unit
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Symbol
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Area
Volume
Density
Velocity
Acceleration
Momentum
Force
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Square metre
Cubic metre
Kilogram per cubic metre meter per second
meter per Square second
Kilogram meter per second
Kilogram “ “ “ Sq.Second
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m2
m3
kg/m3
m/s
m/s2
kg m/s
kg m/s2
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Some physical quantities can be expressed as product of different powers of fundamental (base) quantities. In such expression, the power of a fundamental (base) quantity is called the dimension of the physical quantity in that base. For example velocity can be expressed as Displacement/time = L/T
Accuracy and precision of measuring Instruments:
As every measurements contain errors, the result of a measurement is to be reported in such a manner to indicate the precision of measurement.
The accuracy of a measurement of any physical quantity made by any measuring instrument is a measure of how close the measured value is to the 'true value' of the quantity.
The precision of the measuring instrument denotes up to what 'limit' or 'resolution' the quantity can be measured with the given instrument. The accuracy depends on the errors and also on the precision of the measuring instrument.
Length is measured by using a metre scale divided into 100 parts, called centimetres.
Each centimetre is further divided into ten parts, called millimetres. It gives an accuracy up to 1mm or 0.1 cm.
Vernier Calipers was invented by Pierre Vernier. It gives accuracy up to 0.01 cm or 0.1mm.
Screw Gauge is an instrument used for measuring the diametre of thin wire or similar objects or thickness of glass plate etc. Its accuracy is upto 0.001 cm or 0.01 mm and is commonly called micrometre screw gauge. It works on principle of a screw.
♦ Pitch of the screw is the distance travelled by the tip of the screw for one complete revolution the head. (or) The distance between two adjacent threads is also called the pitch of the screw.
♦ Smallest length that can be measured accurately using an instrument is called least count of that instrument.
♦ Least count of the screw gauge = Pitch of the Screw/No.of HeadScale Division
♦ Thickness of a plane (or) Diameter of a wire = P.S.R + H.S.R × L.C.
♦ If the zeroth division of the head scale does not coincide with the index line, then the screw gauge has zero error.
♦ If the zeroth division of the head scale is above the index line of the pitch line, the error is negative and the correction is posture.
♦ If the zeroth division of head scale is below the index line of the pitch line, the error is positive and the correction is negative.
VERY SHORT ANSWER QUESTIONS (1 Mark)
1. What is the Principle of a Screw gauge?
- Screw gauge works on the principle of a screw in a nut.
2. What is the pitch of a screw?
- The distance travelled by the tip of a screw for one complete rotation of its head is called the pitch of the screw.
3. What is the least count of a screw gauge?
- The least measurement that can be measured by a screw gauge is called its least count.
Short Answer Questions (2 Marks)
1. What is meant by zero error of screw gauge?
- If the zeroth division of the head scale do not coincide with the index line of the pitch scale then the screw gauge is said to have zero error.
2. What is positive error of a screw gauge?
- If the zeroth division of the head scale is below the index line of the pitch scale by 'n' divisions, the error is said to be positive and correction is negative.
3. How do you determine the diameter of a wire using a screw gauge?
- Aim of the experiment: To determine the diameter of a wire using screw gauge.
Apparatus: Screwgauge, wire.
Procedure:
1. Find the pitch of the screw by taking suitable rotations and using formulae,
Pitch of the screw(P.S) = Distance travelled by screw / total.no.of complete rotations
2. Find the least count of the screw gauge by using the following formula?
LC = Pitch of the screw/No.of HeadScale Division = P/N and also determine the zero error of the screw gauge.
3. The given wire is fired between the shafts S1 And
S2
4. The head scale is rotated anti-clockwise.
5. Due to anti-clock wise rotation the shafts open and hold the wire tightly as shown in the figure.
6. Then the value of the pitch scale division which just precedes edge of the head scale is noted as pitch scale reading (P.S.R)
7. The value of the head scale division which just coincides with the index line is the observed head scale reading (H.S.R.)
8. Now, the diameter of the wire d = P.S.R + H.S.R × L.C
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Sl.No
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Odject
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P.S.R
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H.S.R
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C.H.S.R
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C.H.S.R x L.C
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Correct Diameter (Or)
P.S.R.+C.H.S.R+L.C
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1
2
3
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Copper Wire
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SCREW GAUGE
1. What is meant by Screw gauge?
- It is an instrument used for measuring the diameter of very thin wires or similar objects.
Its accuracy is upto 0.001 cm and is commonly called screw gauge.
2. Write the construction of a screw gauge?
- The screw gauge consists of the following parts:
1. U-Frame: It is a steel frame, shaped in the form of U. On one end of U-Frame is fixed a screw permanently. It is commonly called stud and forms the fixed jaw of the screw gauge. On the other end of U-frame is fixed a nut, through which slides a screw. The end B of the screw forms the movable jaw of screw gauge.
2. Nut and screw: The nut is threaded from inside and the screw from outside. The screw can move in and out of nut by circular motion.
3. Thimble or circular cylinder: The screw is connected to a hollow circular cylinder (s) which rotates along with nut on turning.
4. Sleeve Cylinder: To the nut is attached a hollow cylinder, commonly called sleeve cylinder. The spindle of the screw passes through sleeve cylinder.
5. Baseline: A reference line or baseline, graduated is mm, is drawn on the sleeve cylinder, parallel to the axis of nut. It is commonly called main scale or sleeve scale.
6. Circular scale or Thimble Scale: The hollow cylinder moving over the sleeve cylinder is tapered from one end. On the tapered end are made graduations, which are either 50 or 100 in number. The scale marked on sleeve is called circular scale or thimble scale or head scale.
7. Ratchet: The ratchet is attached to screw by means of a spring. When the flattered end B of the screw comes in contact with stud A, the ratchet becomes free and makes a rattling noise. Thus, end B of the screw is not further pushed towards the stud A.
3. Define pitch of the screw and how do you determine pitch of the screw?
1. The pitch of screw is defined as, the distance between two consecutive threads of screw, measured along the axis of screw .
2. Pitch of screw can also be defined as the distance travelled by the tip of screw (end B) when head of screw is given one complete rotations.
Determination: In order to determine pitch, the screw is give five complete rotations. The
distance moved by the thimble on the main scale is recorded. The pitch can be found by the
formula
Pitch = Distance moved by thimble on mainscale/Number of rotations of thimble
- If 5mm is the distance moved by the thimble on the main scale for 5 rotations then: pitch = 5mm / 5 = 1mm
1. What are positive and negative zero error of a screw gauge? How are they
determined?
1. Positive zero error: If the zeroth division of the head scale below the index line of the pitch scales the error is said to be positive and the correction is negative.
Determination: If n is the number of units below the index line, then the correction will be - n units.
∴ corrected H.S.R (C.H.S.R) = observed H.S.R. – n (number of divisions below)
2. Negative zero error: If the zeroth division of the head scale is above the index line of the pitch scale, the error is said to be negative and the correction is positive.
Determination: If n is the number of units above the line, then the correction will be +n units.
∴ Corrected H.S.R. (CHSR) = observed H.S.R + n (number of divisions below)
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