Experimental Physics

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64 of 70

Question 64 of 70

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 ' aa ' units, then the least count of the instrument is

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Answer: (D) aN+1\frac{a}{N+1}

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+1a N=b(N+1) \Rightarrow \mathrm{b}=\frac{a N}{N+1}
Least count is a−b=a−aNN+1\mathrm{a}-\mathrm{b}=\mathrm{a}-\frac{a N}{N+1} =a[N+1−NN+1]=aN+1=a\left[\frac{N+1-N}{N+1}\right]=\frac{a}{N+1}

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