The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions if each main scale division is 0.5 mm. Calculate the minimum inaccuracy in the measurement of distance.

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Solution

Step1: Given data
1 MSD = 0.5 mm
50 divisions of the vernier scale coincide with 49 main-scale divisions
that is
, $50 V D S (v e r n i e r s c a l e d i v i s i o n) = 49 M S D (m a i n s c a l e d i v i s i o n) \Rightarrow 1 V S D = \frac{49}{50} M S D$
Step2: Formula Used
The least count is the minimum possible measurement that could be done using an instrument.
Least Count (L.C.)=
$1 M S D - 1 V S D \Rightarrow 1 M S D - \frac{49}{50} M S D \Rightarrow \frac{1}{50} M S D$
Step3: Calculating the minimum inaccuracy, that is, the least count
$L. C. space equals 1 over 50 M S D L. C. equals 1 over 50 cross times 0.5 space space left square bracket space A s 1 M S D equals 0.5 m m right square bracket rightwards double arrow L. C. space equals space 0.01 space m m$
Hence, the minimum inaccuracy in the measurement of distance is $0.01 m m$

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