Q. In a vernier callipers, 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 callipers is
A) $\left( \frac{n - 1}{n} \right)x$
B) $\frac{nx}{(n - 1)}$
C) $\frac{x}{n}$
D) $\frac{x}{(n - 1)}$
Explanation
One main scale division, $1\ M.S.D.\ = x\ cm$ One vernier scale division , $1\ V.S.D.\ = \frac{(n - 1)x}{n}$ Least count $= 1\ M.S.D.\ - 1\ V.S.D.$ $= \frac{nx - nx + x}{n} = \frac{x}{n}\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.