The main scale of a vernier callipers has n divisions/cm. n divisions

1.	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) \(\frac{1}{n^2}\)
Answer» (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

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) \(\frac{1}{n^2}\)

Answer»

(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