Meter Scale
This simplest instrument to measure length in the laboratory
is a meter scale. Its length is 1 meter or 100 centimeters. Because of this, it
is called a meter scale. One side of this scale is graduated in centimeter and
the other side in inches. Each centimeter is divided into ten equal parts. Each
of these parts is called 1 millimeter or 0.1 centimeter. Each inch is divided
into eight, ten or sixteen equal parts.
Measure
with a meter scale: To measure the length of a rod or a stick by
the meter scale, its one end is so placed that is coincides with the 0 mark or
some other convenient mark of the scale. The reading of the mark that coincides
with the other end of the rod is taken. The difference between the readings at
the two ends of the rod gives the length of the rod. In general if the reading
of the mark that coincides with the left end of the rod is x and that of the
mark coinciding with the right end is y. Then the length of the rod is L = y –
x. With this scale length may be measured to an accuracy of 1 millimeter. For
more accurate measurement vernier scales are used.
Vernier scale
In
the ordinary meter scale we can measure length up to 1 millimeter. To measure
fractions of millimeter like 0.2mm, 0.6mm, 0.8mm etc. we have to use vernier
scale. This scale was invented by a mathematician Pieria Vernier and is called vernier
scale according to his name. |
| Vernier scale |
A small scale is used by the side of the main scale for accurate
measurement of fractions of the smallest division of the main scale. By using vernier
scale along with meter scale fractions of millimeter may be measured
accurately.
Vernier scale can be moved forward or backward along the side of
the main scale. Say, a vernier scale has ten divisions this ten division is
equal to nine smallest divisions of the main scale (fig of vernier scale). Nine
smallest divisions of main scale is 9 millimeter or 0.9 centimeter. As 10 vernier
scale divisions is equal to nine smallest divisions of the main scale. So, a vernier
scale division is slightly smaller than the smallest division of the main
scale. The difference between the smallest main scale division and the vernier
scale division is called vernier constant. It is generally written by VC. A
simple equation may be used to determine the vernier constant, that is vernier
constant = s/n, where s is the length of 1 smallest division of the main scale
and n the number of vernier divisions.
As mentioned above, s = 1 mm and n = 10 divisions
∴ Vernier
constant = s / n = 1 mm / 10 = 0.1mm = 0.01cm.
Sometimes 20 vernier scale divisions are equal to 19 smallest main
scale divisions and the smallest main scale division is less than 1 mm. Then the
vernier constant becomes difference. The vernier constant depends on the
characteristics of marking the main scale and the vernier scale.
Slide Calipers
The other name of slide calipers is vernier
calipers. Because, the Vernier’s method is used for the measurement with this
instrument. The main scale of the slide calipers is made of a graduated
rectangular still plate. A metal jaw is fixed at the starting end of the main
scale, that is, at the end marked 0 of the main scale. A Jawed small scale is
put over the body of the main scale, to measure fraction of the small division
of the main scale accurately. It is called vernier scale. |
| Slide Calipers |
This Jawed vernier scale can be moved forward or backward
along with the main scale. There is screw in it. It can be fixed at any point
on the body of the main scale with this screw. When the Jaw of the vernier
scale touches the Jaw of the main scale then the zero of the main scale should
coincide with the zero of the vernier scale.
By using vernier scale fraction of millimeter may be
measured accurately.
Vernier constant of the slide calipers can determine from
the above mentioned vernier scale chapter.
Measurement of slide calipers: Suppose, the length of
rod is to be measured. The rod is to be placed between the two jaws of
the slide calipers. The jaw connected with the vernier scale is to be pushed
forward so that the jaws of the main scale and the vernier scale touch the
opposite ends of the object. The rod is placed such that its left end coincides
with zero (0) mark of the main scale. The vernier scale is moved forward and
backward to make it coincide with the right side of the rod. Suppose the right
end of the rod has crossed M mm mark of the scale and is between M and (M + 1)
mm. This extra distance beyond M mm is to be determined by using the vernier
scale. This length will be the vernier reading.
Now it is to be noted which vernier scale mark coincides
with which of the main scale mark. If no vernier mark coincides with a main
scale mark then find out the nearest vernier mark. The reading of this mark
that is the number of vernier scale divisions from the left to this mark is the
vernier scale reading.
Suppose the Vth vernier mark coincides with or
nearest with any main scale mark. Hence the vernier constant of the instrument
is VC.
The length of the rod = main scale reading + vernier scale
reading = main scale reading + vernier scale reding x vernier scale constant.
Thus, L = M + V x VC, where VC is the vernier
constant.
The jaw connected with the vernier scale is to be pushed
forward so that the jaws of the main scale and the vernier scale touch the
opposite ends of the object. In some instrument reading not is coincided. Then
have to understand there are some errors in the instruments and have to rectify
it.
Screw Gauge
This is device for the measurement of radius of
wire of this cylinders and small length. It consists of a u-shaped still frame. |
| Screw Gauge |
The rod with plane end is permanently fixed with the plane surface
A of one arm. The other arm has a hollow cylinder C. A linear scale graduated
in millimeter is marked on the cylinder and a screw with a cylindrical cap T is
fitted with it. The screw can move through the hollow cylinder C. The end of
the cylindrical cap T is graduated 0 to 50 or 100. When the Jaws are closed,
that is, then the head of the screw B touches the plane end of the fixed rod A,
the zero of the circular scale coincides with the zero of the linear scale. If
the zero marks of the two scales do not coincide, then there is instrumental
error.
The distance through which the screw advances along the
linear scale when the cap T is rotated once is called the Pitch of the screw
gauge. The distance through which the screw advances when the circular scale is
rotated through only 1 division is called the least count. The least count is
obtained by dividing the pitch by the number of divisions in the circular
scale.
Usually the circular scale has 100 divisions and the pitch is 1 mm.
Measurement by Screw
Gauge: The wire
whose diameter is to be measured or the plate whose thickness is to be
determined is placed between A and B. The wire or the plate should be so placed
that it’s one side touches A and the other side touches B. Now the reading of
the linear and circular scales is to be taken. Suppose the reading of the
linear scale 1 mm, and the number of divisions of the circular scale is C. Then
the diameter of the wire or the thickness of the plate will be:
Diameter or thickness = Linear scale reading + no. of
divisions of the circular scale x Least count.
That is, D = L + C x LC
When the head of the screw touches the plane end of the
fixed rod A, then the zero of the circular scale should coincide with the zero
of the linear scale, then it means there is an error. For this reading should
be corrected.
Balance
Sometimes in physics and chemistry the mass of a
small quantity of a substance needs to be measured very accurately, this is not
possible with a common balance. The less quantity of the substance, the more
accurate the balance should be. The balance is such an accurate weighting
machine. This instrument is used in physics and chemistry laboratories for
accurate measurement of small masses. Because, if the measurement of the mass
in the laboratory is not accurate, the result will be wrong and the objective
of the experiment will not be fulfilled. |
| Balance |
The balance has two scales pans P1 and P 2
of equal weight at the two ends like an ordinary balance. The scale pans are
hanged from the ends of a metal beam AB with the help of two frames of equal
weight. The frames are placed on two inverted knife edges in two grooves at the
end.
A knife with its edges downward is fixed in the middle of the beam
AB. It is placed on a hollow vertical pillar. The pillar is firmly fixed at the
middle of a wooden floor CC. Three leveling screws LS are fixed with this floor
(the third has not been shown in the fig.). These are used to level the
instrument. A solid metal rod inside the hollow pillar can be raised or lowered
with the help of a level H connected with the floor. The base of triangular
shaped agate is fixed exactly in the middle of the beam AB. The sharp age is
kept on an agate plate placed on the solid rod of the beam. When the solid rod
is lifted, the beam AB swings about the narrow edge of the agate as the
fulcrum.
The broad side of a long pointer (PO) is fixed at the middle of
the balance. Its lower narrow end is free to move over a scale. When the beam
is horizontal, the pointed end of the pointer rests on the zero of the scale.
The beam is made horizontal with the help of a plumb-line (PL) and the leveling
screws. The entire instrument is kept in a glass box.
Measurement by Balance: To use the balance, the handle H is
rotated to left the pillar and hence the beam AB .The beam will then
start swing freely about the knife edge. Along with the beam the scale pans
will also keep in swinging up and down, with the backward rotation of the
handle H. The pillar will be lowered and the swinging of the beam and scale
pans will stop.
When the beam AB swings, the lower end of the pointer keeps
oscillating right and left over the scale. If there is nothing on the scale
pan, the oscillation of the pointer should be equal on the two sides of the
zero of the scale. If it is not, the two adjusted screws (BS) at the two ends
of the beam AB are to be so adjusted that the oscillation of the pointer on the
two sides of the zero of the scale becomes equal. Whether the pillar P is
vertical or not is seen with the plumb-line PL.
To measure the mass of an object it is placed on the left-hand
pan. Known weights are placed slowly on the right-hand pan one by one, till the
pointer oscillates equally to the two sides of the zero of the scale. Thus the
mass of an object is determined with the help of known weights.
Stopwatch
Stopwatch is used to measure small time interval. Stopwatches are
of two kinds’ digital stopwatch and analog stopwatch. Digital stopwatch can
give more accurate reading than that of analog stopwatch. An analog stopwatch
can give an accurate reading up to ±0.15 while a digital stopwatch can read
accurately up to ±0.015. Now a day’s digital stopwatch is found in mobile phone
also.
A stopwatch has to start and stop by the hands to measure a time.
An error of about a large fraction of a second takes place in the reading of
time interval though it may vary from person to person. The degree of error is
more to the old than the young. For most of the people the error is about
0.3seconds.
Error and accuracy in measurement
All measurements have some limitations of accuracy. Accuracy of
measurement depends on the skill of observer and the instruments used. Suppose
a meter scale is graduated in centimeter and millimeter. If we want to measure
the length of this book we will get the result probably up to 0.1cm accurately.
In Accuracy may be reduced in case of measuring the length of a house because
the scale is to be used several times for measuring the full length. Every time
the position of the front edge of the scale has to be marker on the floor. This
increases the source of error thus increasing the probability of errors.
The accuracy of measurement is as important as measurement itself.
So, the observer should mention the degree of accuracy of result with the
result of the experiment. Let the length of this book be 26.0cm ±0.1cm. Here
the symbol ±means that the real length of the book is between 25.9cm and
26.1cm. Here 0.1cm is the uncertainty or error of measurement.
Generally there are three types of error in measurement. There
are:
1.
Random error
2.
Instrumental error
3.
Personal error
Random error: The error for which irrelevant occur in
measured results by measuring a constant quantities. Several times is
random error. The word random itself implies that the error cannot be guessed
earlier and expected value will be zero. This is because measured values moves
around the accurate value and average value of the errors should be zero if the
value of the quantity is measured by the same instrument. The random error will
be included as much as many times the scale is used to measure the floor. Each
time the front edge marking on the floor falls a little back and forth of the
accurate mark. Another random error takes place with the measurement when the
meter scale is placed at the previous marking (slightly error position) as back
edge starts from back and forth position. The final result may be very much
high or low due to random error. It is impossible to avoid random error but
this error can be reduced by precautionary measurement. In order to minimize
the random error average of the frequent measurement is to be taken.
Instrumental error: We need instruments for experimental
measurement in physics. The error with the instrument is called
instrumental error. For example, if the zero marking of main scale is not
super-imposition with the zero marking vernier then the result of measurement
will not be accurate. This kind of error is known as instrumental error.
Similarly if the indicator needle of ammeter or voltmeter is not
super-imposition with the zero marking then there remains error with the
instrument. The instrumental error has to be determined before starting the
experiment. Finally the actual reading has to be obtained by subtracting this
error from the reading.
Personal error: We have to take various readings during
experiment. The error that an experimenter makes during experiment is
called personal error. The error with the position of the observer, observing
any mark or any calculation is also said to be personal error. For example
there will be an error while measuring the length of a rod if the
super-imposition of the edge of a rod with a definite mark of the scale is
observed obliquely instead of perpendicular position. There will be error in
reading when we cannot observe which division of circular scale is in
super-imposition with the linear scale of a time per screw gauge. Similarly we
cannot find accurate if there is mistake in counting oscillation number while
determining time period of a pendulum. All these are known as personal errors.
We have to take the reading properly and carefully with a view to avoiding
these errors.
End
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