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Q.

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

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a

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

b

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

c

$a (N - 1) units$

d

$\frac{a}{N} units$

answer is C.

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Detailed Solution

$(n + 1) V S D = N M S D$

$1 V S D = (\frac{N}{N + 1}) a$

$But L C = 1 M S D - 1 V S D$

$L C = a - (\frac{N}{N + 1}) a = (\frac{a}{N + 1})$

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