♡ In a vernier calipers, p divisions of its main scale match with (p

1.	♡ In a vernier calipers, p divisions of its main scale match with (p+1) divisions onits vernier scale. Each division of the main scale is k units. Using the vernier principle, its least count will be♡¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤
Answer» Given: <P>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: $\red{ \boxed{ \blue{ \large{ \rm{ LC = \dfrac{k}{p + 1} }}}}}$