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N divisions on the main scale of a vernier calipers coincide with (N + 1) divisions on vernier scale. If each division on main scale is of ‘a’ units, then least count of the instrument is _____

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$\frac{a}{N - 1}$

$\frac{a}{N}$

$\frac{a}{N + 1}$

$\frac{a}{2 N}$

answer is C.

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Detailed Solution

$1 VSD = (\frac{N}{N + 1}) MSD = (\frac{N}{N + 1}) a$
LC = 1 MSD – 1 VSD
$= a - \frac{a N}{N + 1}$
$= \frac{a}{N + 1}$

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