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The nth divis...

Question

The nth division of main scale coincides with (n + 1)th divisions of Vernier scale. Given one main scale division is equal to a units. Find the least count of the vernier.

A

\frac{2 a}{a + 1}

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B

\frac{a}{a + 1}

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C

\frac{3 a}{a + 1}

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D

\frac{a}{2 a + 1}

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Solution

The correct option is B $\frac{a}{a + 1}$
$(n + 1)$ division of vernier scale= n divisions of main scale.
$∴$ One vernier divisions $= \frac{n}{n + 1}$ main scale divisions
Least count $= 1 M . S . D - 1 V . S . D = (1 - \frac{n}{n + 1})$ M.S.D
$= \frac{1}{n + 1} M . S . D = \frac{a}{a + 1}$

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