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I.G.C.S.E Physics
Measurements
❖ A measure is a reference standard for comparing physical quantities. It consists of two parts
a NUMBER and a UNIT.
❖ Least count (L.C): Least count is the smallest possible measure that an instrument can make.
❖ Significant figure: Significant figures are all the digit of a number that are used to express it to
the required degree of accuracy, starting from the first non-zero digit.
❖ Measuring length:
A meter rule:
Least count: 0.1cm
Vernier calliper:
Least count: 0.01 cm
Micrometer screw gauge:
Least count: 0.001 cm
1. Measuring the thickness of a sheet of paper
Whenever measuring a very minute quantity (very close to the least count of the instrument or
even smaller) the margin for error is huge. In order to avoid such error, we prefer taking a larger
number of objects together and then making the measurement.
Eg. Measuring the thickness of a sheet of paper:
• Check for zero error on your instrument.
• Take a number of sheets together (roughly 20 to 30 sheets).
• Measure the thickness of the bunch using appropriate instrument (preferably micro meter screw
gauge).
• Divide the result by the number of sheets.
• Make the measurement at different places on the sheet (as the thickness may not be the same
everywhere on the sheets) and take an average.
Note: You can use similar method for other quantities as well only your instrument would
change.
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Using a vernier calliper:
The method of using a vernier calliper is as follows:
• Close the calliper such that it jaws firmly hold the object. But make sure that the object is not
clamped too tight, it might deform the object.
• Look at the zero on the vernier scale. Read the main scale, just to the left of the zero. This will
give you the main scale reading (Generally millimetres)
• Now look at the vernier scale. Find the point where one of its markings is exactly aligned with
one of the markings on the main scale. Read the value of the vernier scale. This tells you the
fractional reading between the markings in the main scale.
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The value of the length is given by adding ‘(vernier scale reading x Least count)’ to the main
scale.
Below diagram illustrates the same.
• Measuring volume:
1. Measuring the volume of a liquid:
The apparatus used in measuring the volume of a liquid is a measuring cylinder.
The following are the steps involved in measuring the volume of the liquid
• Take a measuring cylinder of appropriate size (Depending on the volume that you want to
measure)
• Carefully pour the liquid into the measuring cylinder without splashing or spilling any.
• Read the marking on the measuring cylinder which is touched by the lower meniscus of the
liquid, this is the volume of the liquid.
• View the reading keeping your eyes perpendicular to the measuring cylinder in order to avoid
parallax/ line of sight error.
2. Measuring volume of solids:
• Regular solids:
If the solid is regular in shape, we measure the dimensions of the object and use respective
formula to find its volume.
Eg: for a cube you measure its sides and the use ‘V= length x breath x height’. For a sphere find
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the radius and use 𝑉 = 𝜋𝑟 3
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• Measuring volume of irregular solids:
For measuring the volume of an irregular solid following step should be followed:
o Take a measuring cylinder or a displacement jar of appropriate size.
o Fill it with a known volume of water (enough for the object to be completely submerged
without spilling the water out).
o Slowly immerse the object into the liquid, without spilling or splashing the water out.
o Read the volume of the water after the object is completely immersed.
o The difference between the original volume and final volume after immersion will give us the
volume of the object.
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If the object floats in water:
If the object floats in water, e.g. Wood, you use a sinker (Any heavy load that can sink your
object because of its weight). The following steps are supposed to be followed:
Immerse the sinker carefully into the water and read the volume.
Tie the object to the sinker and immerse it again reading the second volume.
The difference between both the volumes will give us the volume of the object.
Calculate the density of the object using the formula, Density = Mass/volume.