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

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

Solution:

Vernier constant = value of $1 \,M.S.D$. - value of $1 \,V.S.D$.
Now $n$ V.S.D. $=(n-1) \text { M.S.D. } $
$=(n-1) \,x \,cm $
$\therefore \, 1\,V.S.D. =\left(\frac{n-1}{n}\right) \,x \,cm$
$\therefore V . C .=x\, cm -\left(\frac{n-1}{n}\right) \,x\, cm $
$=\frac{x}{n}\, cm$