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

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

$\frac{x}{n}$

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

answer is C.

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Detailed Solution

Vernier constant = value of 1 M.S.D - value of 1 V.S.D.

Now n V.S.D = (n - 1) M.S.D = (n - 1) x cm

$∴ 1 V . S . D = (\frac{n - 1}{n}) x c m ∴ L . C . = x c m - (\frac{n - 1}{n}) x c m = \frac{x}{n} c m$

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