Ch1 MEASUREMENTS & EXPERIMENTATION
 The least count of an instrument is the smallest measurement that can be taken accurately with
it.
 The smaller the least count of an instrument, the more accurate the measurement made by using
it.
 E.g., for a metre rule the smallest measurement is one-tenth of a centimetre or 1 mm.
 A stop watch has a least count of 0.5 s if there are 10 divisions between the 0 s and 5 s mark.
 Since the metre rule or student scale is not precise, other instruments were developed
to measure length such as the Vernier Callipers and the Screw Gauge.
 Using a Vernier calliper, one can measure the thickness, depth and length of objects.
 he Vernier callipers was an instrument designed by French physicist Pierre Vernier. It
has two scales – the main scale and the Vernier scale which slides over the main scale.
 The main scale is like a regular metre scale whose smallest division is 1 mm. The
Vernier scale generally has 10 divisions. There are two sets of jaws – two fixed and two
movable ones.
PART
FUNCTION
Outside Jaws
Measures length of rod, diameter of sphere,
external diameter of hollow cylinder
Inside jaws
Measures internal diameter of hollow cylinder
Strip
Measure depth of a beaker or bottle
Main Scale
To measure length correct up to 1 mm
Vernier Scale
Measures length correct up to 0.1 mm
 Vernier Constant: The least count of vernier is equal to the difference between the
values of one main scale division and one vernier scale division. This is also known as
the vernier constant.
 The least count of a Vernier calliper is obtained by dividing the value of one division of
the main scale by the total number of divisions on the Vernier scale.
 The Vernier callipers are so designed such that ‘n’
divisions on the Vernier scale correspond to ‘n-1’
 Thus, value of 1 division on Vernier scale =
𝒏 −𝟏 𝒙
𝒏
 Least Count (LC) of Vernier Calliper = 1 MSD – 1 VSD
divisions on the main scale.
 Value of n divisions on the VS= value of (n - 1)
divisions on the MS
𝑥
nx −x n−1
=
𝑛
n
 LC = x – (𝑛 − 1)
 LC =
=
nx − nx + 𝑥
n
𝑥
𝑛
 If value of 1 division on the MS is x,
 Where, n is the number of divisions on the Vernier Scale
 then value of (n - 1) divisions is (n - 1) x  Thus, value
of n divisions on the VS = (n - 1) x
and x is the value of one main scale division.
 Generally, 1 MSD is 1 mm, and the number of divisions on the Vernier scale are 10.
 Thus, LC of Vernier Scale having 10 divisions on the VS = 1/10 = 0.1 mm or 0.01 cm (as 10
mm = 1 cm or 1 cm = 0.1 mm).
 Length = Main Scale Reading + (Least Count x p)
Where p is the division number of the vernier scale that aligns with the Vernier Scale
 Due to wear and tear and incorrect use, the zero mark of the Vernier scale does not coincide with the zero mark of the main scale,
when the jaws are brought together (no object is clamped between them).
 The two types of zero errors are
 Positive zero error (+): when the Vernier scale zero is to the right of main scale zero. This means that the Vernier scale appears
to be reading an extra value which needs to be deducted from the total reading to correct the overall reading
 Negative zero error (-): when the Vernier scale zero is to the left of main scale zero. This means that the Vernier scale appears
to be reading lesser value which needs to be added to the total reading to correct the overall reading
Zero error = Division# aligning with main scale * L.C.
Corrected reading = observed reading – ZE (with sign)