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

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

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

$\frac{1}{n} cm$

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

answer is C.

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Detailed Solution

$\begin{array}{l} nVSD = (n - 1) MSD; 1 VSD = \frac{(n - 1)}{n} MSD \\ L . C . = 1 MSD - 1 VSD = 1 MSD - \frac{(n - 1)}{n} MSD \\ = \frac{1}{n} MSD = \frac{1}{n} \times \frac{1}{n} cm \\ = \frac{1}{n^{2}} cm \end{array}$

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