A) a
B) \[\frac{a}{N}\]
C) \[\frac{N}{N+1}\times a\]
D) \[\frac{a}{N+1}\]
Correct Answer: D
Solution :
| [d] 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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