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The main scale of a vernier calliper has n divisions/ cm. n divisions of the vernier scale coincide with $(n - 1)$ divisions of main scale. The least count of the vernier calliper is,

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$\frac{1}{n} cm$

$\frac{1}{n^{2}} cm$

$\frac{1}{n (n + 1)} cm$

$\frac{1}{(n + 1) (n - 1)}$

answer is C.

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Detailed Solution

$1 MSD = \frac{1}{n} cm$

$n (VSD) = (n - 1) MSD$

$VSD = \frac{n - 1}{n} MSD$

Least count $= 1 MSD - 1 VSD$

$= [1 - \frac{(n - 1)}{n}] MSD$

$= \frac{1}{n} \cdot \frac{1}{n} = \frac{1}{n^{2}} cm$

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