Question

In a Vernier Calipers (VC), $N$ divisions of the main scale coincide with $N+m$ divisions of the vernier scale. What is the value of $m$ for which instrument has least count $0.01mm$?

• A. $1$
• B. $N$
• C. Infinite
• D. $N/2$

Answer 1

Answer: (A)

$1$

We know that least count of the vernier callipers $=1M.S.D-1V.S.D$.
But since we are given that $N$ divisions of the main scale coincide with $N+m$ divisions of the vernier scale, we have:
$N$ divisions of $M.S.D=N+m$ divisions of $V.S.D$ and,
$1V.S.D=\frac{N}{N+m}M.S.D$
Now, $L.C=1M.S.D-\left(\frac{N}{N+m}\right)M.S.D$ or
$L.C=\frac{m}{N+m}M.S.D$
Thus, for a minimum least count that is $0.001cm$ or $0.01mm$, the value of $m$ should be $1$.