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The main scale of a vernier calipers reads in millimeter and its vernier scale is divided into 10 divisions which coincide with 9 divisions of the main scale. When the two jaws of the instrument touch each other the seventh division of the vernier scale coincide with a scale division and the zero of the vernier lies to the right of the zero of the main scale. Furthermore, when the cylinder is tightly placed along its length between the two jaws, the zero of the vernier sale lies slightly to the left of 3.2 cm; and the fourth vernier division coincides with a scale division. What will the measured length of the cylinder be?

$\begin{array}{1 1} 3.14\;cm \\ 3.09\;cm \\ 3.07 \;cm \\ 3.31 \;cm \end{array}$

1 Answer

Vernier constant $= \large\frac{1}{N}$$S = \large\frac{1}{10}$$ = 0.1mm$
The instrument has a positive error which is $e = NC = 7 \times 0.1mm = 0.07cm$
Vernier scale reading $= 4 \times 0.01 = 0.04cm$ (since the fourth vernier division coincides with a scale division)
Therefore, the observed reading = $3.1 + 0.04 = 3.14cm$
The true reading, adjusting for error is $ = 3.14 - 0.07 = 3.07cm$
answered Apr 2, 2014 by balaji.thirumalai

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