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Physics Question on physical world

In a slide callipers, (m+1)(m + 1) number of vernier divisions is equal to m number of smallest main scale divisions. If d unit is the magnitude of the smallest main scale division, then the magnitude of the vernier constant is

A

d(m+1)\frac{d}{\left(m+1\right)} uint

B

dm\frac{d}{m} uint

C

md(m+1)\frac{md}{\left(m+1\right)} uint

D

(m+1)dm\frac{\left(m+1\right)d}{m} uint

Answer

d(m+1)\frac{d}{\left(m+1\right)} uint

Explanation

Solution

(m+1)(m+1) vernier division =m=m main scale division One division on vernier scale =(mm+1)=\left(\frac{m}{m+1}\right) division on main scale Vernier constant =(1−mm+1)d=dm+1=\left(1-\frac{m}{m+1}\right) d=\frac{d}{m+1}