Question

♡ In a vernier calipers, p divisions of its main scale match with (p+1) divisions on

its vernier scale. Each division of the main scale is k units. Using the vernier

principle, its least count will be♡

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Answer 1

Given:

In the vernier calliper, p th division of main scale match with (p+1) th division of the vernier scale.Each division of main scale is k units.

To find:

Least count of the instrument

Calculation:

Least count vernier caliper is defined as 1 main scale division -1 vernier scale division.

Main scale division is denoted by MSD , Vernier scale division is denoted as VSD;

$\sf{p(MSD) = \{(p + 1)(VSD) \}}$

$\sf{ = > 1 \: VSD = \dfrac{p(MSD)}{p + 1} }$

$\sf{ = > 1 \: VSD = \dfrac{pk}{p + 1} }$

Let least count be LC

$\sf{LC = 1 \: MSD - 1 \: VSD}$

$\sf{ = > LC = k - \dfrac{pk}{p + 1} }$

$\sf{ = > LC = k \bigg(1 - \dfrac{p}{p + 1} \bigg)}$

$\sf{ = > LC = \dfrac{k}{p + 1} }$

So, final answer is:

$\red{ \boxed{ \blue{ \large{ \rm{ LC = \dfrac{k}{p + 1} }}}}}$

Answer 2

Answer:

the least count will be K/p+1

I hope it helps you