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 the instrument has minimum least count?

• A. 0
• B. N
• C. Infinity
• D. N/2

Answer 1

The correct option is A 0

$N(m\cdot s\cdot D)=(N+m)V\cdot s\cdot D$

$\begin{array}{c}\text{1VSD}=\frac{N}{N+m}MSD\\ L\cdot C=\text{1MSD}-1VSD\end{array}$

$=(1-\frac{N}{N+m})MSD$

$L\cdot C=\frac{m}{N+m}\text{vsD}$

$\begin{array}{c}\text{For min}L\cdot C,\frac{m}{N+m}\text{should be minimum.}\\ \text{let}\\ \text{diferentiating and puting equal to zero:}\\ \text{(wrt m)}\end{array}$

$\begin{array}{c}\frac{(N+m)\times 1}{(N+m{)}^2}=1\times m=0\\ \text{According to the given question no such value possible.}\end{array}$