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Question
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
A Diagram of the vernier calliper is shown below.
According to the problem, 50 divisions of the Vernier scale coincide with 49 main scale divisions.
50 VSD = 49 MSD
⇒ 1 MSD = `50/49` VSD or 1 VSD = `49/50` MSD
Where MSD = Main scale division and VSD = Vernier scale division.
We know that
Minimum inaccuracy = Vernier constant
= 1 MSD – 1 VSD
= 1 MSD – `49/50` MSD = `1/50` MSD
It is given in the problem that 1 MSD = 0.5 mm
Hence, minimum inaccuracy = `1/50 xx 0.5` mm = `1/100` = 0.01 mm
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