Question

The main scale division of a vernier calipers is equal to $p$ unit and the $(m+1)$th division of a vernier scale coincides with the $m$th division of the main scale. The least count of the vernier is:

• A. $\frac{ma}{m+1}$
• B. $\frac{m}{m+1}$
• C. $\frac{a}{m+1}$
• D. $\frac{p}{m+1}$

Answer 1

The correct option is D $\frac{p}{m+1}$

It is given that $(m+1{)}^{th}$ division of the vernier scale division coincides with the $m^{th}$ division of the main scale.

Least count of the main scale is $p$ unit i.e. $1M.S.D.=p$ unit

So, least count of vernier caliper $L.C.=1M.S.D.-\frac{m}{m+1}\times 1M.S.D.$

$⟹L.C.=p-\frac{m}{m+1}\times p=\frac{p(m+1)-mp}{m+1}=\frac{p}{m+1}$ unit