Question

In a vernier calliper, one main scale division is $xcm$ and $n$ divisions of the vernier scale coincide with $(n-1)$ division of the main scale. The least count (in cm) of the callipers is.

• A. $\left(\frac{n-1}{n}\right)x$
• B. $\frac{nx}{n-1}$
• C. $\frac{x}{n}$
• D. $\frac{x}{n-1}$

Answer 1

Answer: (C)

$\frac{x}{n}$

$\begin{array}{cc}& \text{I MSD}=xcm\\ & \end{array}$

$\left(n\right)V.s.D=(n-1)MSD$

$\begin{array}{cc}1VSD& =\frac{n-1}{n}\text{MSD}\\ & =\frac{n-1}{n}xcm\\ L\cdot C=& \text{1 MSD}-\text{1 VSD}\end{array}$

$\begin{array}{c}=x-\left(\frac{n-1}{n}\right)x\\ =\frac{nx-(n-1)x}{n}\\ =\frac{x}{n}cm.\end{array}$