A) a
B) \[\frac{a}{N}\]
C) \[\frac{N}{N+1}\times a\]
D) \[\frac{a}{N+1}\]
Correct Answer: D
Solution :
No of divisions on main scale = N No of divisions on vernier scale = N+ 1 size of main scale division = a Let size of vernier scale division be b then we have\[aN=b(N+1)\Rightarrow b=\frac{aN}{N+1}\] Least count is \[a-b=a-\frac{aN}{N+1}\] \[=a\left[ \frac{N+1-N}{N+1} \right]=\frac{a}{N+1}\]
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