Question

In a Vernier caliper, $N$ divisions of vernier scale coinsides with $(N-1)$ divisions of main scale in which the length of $1$ division is $1mm$. The least count of the instrument (in $cm$) is

• A. $N$
• B. $N-1$
• C. $\frac{1}{10N}$
• D. $\frac{1}{N}-1$

Answer 1

The correct option is C $\frac{1}{10N}$

$1MSD=1mm$

$NVSD=(N-1)MSD$

$\therefore 1VSD=\left(\frac{N-1}{N}\right)MSD$

Since least count is give by:
$LC=1MSD-1VSD$

$=1MSD-\left(\frac{N-1}{N}\right)MSD$

$=\frac{1}{N}MSD$

$=\frac{1}{N}mm(\because 1MSD=1mm)$

$\Rightarrow L=\frac{1}{10N}cm$