Question

if n vernier scale division coincide with (n-1) main scale division then the least count of the vernier calliper is

Answer 1

n div in v s = n-1 msd

1 vsd =(n-1)/n msd
LC=1 msd-1 vsd
=1-(n-1)/n
=0.01 cm (10 msd=1 cm)

Answer 2

Least Count of vernier callipers is 1/(n-1)

Explanation:

Given n vernier scale division coincide with n - 1 main scale division

Therefore,

If the main scale is s and vernier scale is v then

$(n-1)v=ns$

Least Count is given by

Least Count (LC) = length of 1 division on vernier scale - length of 1 division on main scale

$LC=v-s$

$\implies LC=\frac{ns}{n-1}-s$

$\implies LC=\frac{s}{n-1}$

Therefore, least count is (1 main scale division)/(n-1)

Hope this answer is helpful.

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