One main scale division of a vernier calipers is ' a ' cm and ${n}^{\text{th }}$ division of the vernier scale coincide with $(n-1{)}^{\text{th }}$ division of the main scale. The least count of the calipers (in mm ) is:

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YESPYQ · Accepted Answer

Correct answer: c) $\frac{10a}{n}$. $$ (n-1) M S D=n V S D \Rightarrow V S D=\frac{n-1}{n}(M S D) $$ Now, L.C $=[1 \mathrm{MSD}-1 \mathrm{VSD}] \mathrm{cm}$ $$ \begin{aligned} & =a-\frac{n-1}{n} a=\frac{a}{n} \mathrm{~cm} \ & =\left(\frac{10 a}{n}\right) \mathrm{mm} \end{aligned} $$

One main scale division of a vernier calipers is ' a ' cm and \({n}^{\text{th }}\) division of the vernier scale coincid…

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