If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier callipers, when each centimetre on the main scale is divided into five equal parts, will be :
If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier callipers, when each centimetre on the main scale is divided into five equal parts, will be :
Show Hint
- \( {2 \over {n + 1}} \) mm
- \( {5 \over {n + 1}} \) mm
- \( {1 \over {2n}} \) mm
- \( {1 \over {5n}} \) mm
The Correct Option is A
Solution and Explanation
Step 2: \( n\) MSD \( =(n+1) \) VSD \( \Rightarrow 1\ \text{VSD}=\frac{n}{n+1}\,\text{MSD} \).
Step 3: Least count \( =1\ \text{MSD}-1\ \text{VSD}=\left(1-\frac{n}{n+1}\right)\text{MSD}=\frac{1}{n+1}\text{MSD} \).
Step 4: \( \text{LC}=\frac{2}{n+1}\ \text{mm} \).
Answer: (A) \( \frac{2}{n+1} \) mm
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