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.

Monjur Alahi

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,

(A) \(\frac{1}{n(n+1)}\) cm

(B) \(\frac{1}{(n+1)(n-1)}\) cm

(C) \(\frac{1}{n}\)

(D) \(\frac{1}{n^2}\)


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Salim Ahmed Kawsar

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(D) \(\frac{1}{n^2}\)

1 V.S.D. = \(\frac{(n-1)}{n}\) M.S.D.

LC. = 1 M.S.D. – 1 V.S.D.

= 1 M.S.D. – \(\frac{(n-1)}{n}\) M.S.D.

= \(\frac{1}{n}\) M.S.D.

= \(\frac{1}{n}\times\frac{1}{n}\) cm

∴ L.C. = \(\frac{1}{n^2}\) cm

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