One main scale division of a vernier callipers is a cm and n ^{text {th }} division of vernier scale

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One main scale division of a vernier callipers is $a$ $cm$ and $n ^{\text {th }}$ division of the vernier scale coincide with $( n -1)^{\text {th }}$ division of the main scale. The least count of the callipers in $mm$ is

A

$\frac{10 na }{( n -1)}$

B

$\frac{10 a }{( n -1)}$

C

$\left(\frac{ n -1}{10 n }\right) a$

D

$\frac{10 a }{ n }$

(JEE MAIN-2021)

Solution

$(n-1) a=n\left(a^{\prime}\right)$

$a^{\prime}=\frac{(n-1) a}{n}$

$\therefore L \cdot C \cdot=1 M S D-1 VSD$

$=\left(a-a^{\prime}\right) c m$

$=a-\frac{(n-1) a}{n}$

$=\frac{n a-n a+a}{n}=\frac{a}{n} c m$

$=\left(\frac{10 a}{n}\right) m m$

Standard 11

Physics

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