One main scale division of a vernier callipers is 'a' cm and nth division of the vernier scale coincide with (n – 1)th division of the main scale.
Question:
One main scale division of a vernier callipers is ' $\mathrm{a}$ ' $\mathrm{cm}$ and $\mathrm{n}^{\text {th }}$ division of the vernier scale coincide with $(\mathrm{n}-1)^{\text {th }}$ division of the main scale. The least count of the callipers in $\mathrm{mm}$ is :
Correct Option: , 4
Solution:
$(\mathrm{n}-1) \mathrm{a}=\mathrm{n}\left(\mathrm{a}^{\prime}\right)$
$a^{\prime}=\frac{(n-1) a}{n}$
$\therefore$ L.C. $=1 \mathrm{MSD}-1 \mathrm{VSD}$
$=\left(a-a^{\prime}\right) c m$
$=a-\frac{(n-1) a}{n}$
$=\frac{n a-n a+a}{n}=\frac{a}{n} \mathrm{~cm}$
$=\left(\frac{10 \mathrm{a}}{\mathrm{n}}\right) \mathrm{mm}$
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