Question

The smallest division on the main scale of vernier callipers is $1 mm$ and $10$ vernier divisions coincide with $9$ scale divisions. While measuring the length of a line, the zero mark of the vernier scale coincides with a main scale division. Determine the least count of the callipers.
A. $0.01 cm$
B. $0.001 cm$
C. $0.02 cm$
D. $0.002 cm$

Answer 1

Hint:from the relation between the vernier scale division and main scale division, obtain 1 vernier scale divisions and use the value to obtain the least count of the vernier scale.The main use of Vernier calipers is to measure the internal and external dimensions or distance extremely accurately.

Formula used:
Least count of vernier scale $ = $1 MSD $ - $ 1 VSD,
where MSD is main scale division and VSD is vernier scale division.

Complete step by step answer:
From the given question, we know that the 10 vernier scale divisions (VSD) are equivalent to 9 divisions of the main scale (MSD). We can obtain 1 vernier scale divisions from this relation,
$10\;{\rm{VSD}} = 9\;{\rm{MSD}}$
Rewrite the above equation, we get,
$
{\rm{1}}\;{\rm{VSD}} = \dfrac{9}{{10}}\;{\rm{MSD}}\\
\Rightarrow{\rm{1}}\;{\rm{VSD}} = {\rm{0}}{\rm{.9}} \times 1\\
\Rightarrow {\rm{1}}\;{\rm{VSD}} = 0.9\;{\rm{mm}}
$
The least count of the vernier caliper is as follows,
\[{\rm{LC}} = 1\;{\rm{MSD}} - 1\;{\rm{VSD}}\]
Substitute the values in the above equation, we get,
\[
{\rm{LC}} = 1\;{\rm{mm}} - 0.9\;{\rm{mm}}\\
\therefore{\rm{LC}}= {\rm{0}}{\rm{.1}}\;{\rm{mm}}
\]
Thus, the least count of the vernier caliper is 0.01 cm and option (A) is correct.

Note:The minimum value of the physical distance that can be measured by a vernier Caliper is termed as the least count or the vernier constant of vernier Caliper and the least count of the vernier scale can be obtained by the ratio of the one main scale division to the total number of Vernier scale divisions.