Question

In a Vernier callipers, N division of Vernier co-inside with (N-1) divisions of main scale in which the length of 1 division is 1 mm. 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 $\frac{1}{10N}$

$1MSD=2mmNVSD=(N-1)MSD\therefore 1VSD=\left(\frac{N-1}{N}\right)MSD$
Since least count is,
$L=1MSD-1VSD=1MSD-\left(\frac{N-1}{N}\right)MSD=\frac{1}{N}MSD=\frac{1}{N}mm(\because 1MSD=1mm)\Rightarrow L=\frac{1}{10N}cm$