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Physics Question on physical world

NN divisions on the main scale of a vernier calliper coincide with (N+1)(N+1) divisions of the vernier scale. If each division of main scale is ′a′'a' units, then the least count of the instrument is

A

aa

B

aN\frac{a}{N}

C

NN+1×a\frac{N}{N+1}\times a

D

aN+1\frac{a}{N+1}

Answer

aN+1\frac{a}{N+1}

Explanation

Solution

No of divisions on main scale =N= N No of divisions on vernier scale =N+1= N + 1 size of main scale division =a= a Let size of vernier scale division be bb then we have aN=b(N+1)⇒b=aNN+1aN=b\left(N+1\right) \Rightarrow b=\frac{aN}{N+1} Least count is a−b=a−aNN+1a - b =a-\frac{aN}{N+1} =a[N+1−NN+1]=aN+1=a\left[\frac{N+1-N}{N+1}\right]=\frac{a}{N+1}