Question

In a vernier calipers, one main scale division is $x \,cm$ and $n$ division of the vernier scale coincide with $( n -1)$ divisions of the main scale. The least count (in $cm$ ) of the calipers is:

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

Answer 1

Answer: (C)

One main scale division, $1 \,M.S.D = x \,cm$
One vernier scale division, $2 \,V.S.D =\frac{( n -1) x }{ n }$
Least count $=1 \,M.S.D -1 \,V.S.D$
$=\frac{nx-nx+x}{n}=\frac{x}{n} cm$