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NEET · Physics · STD 11 - 1. units,dimensions and measurement
The main scale of a vernier calliper has \(n\) divisions/ \(\mathrm{cm}\). \(n\) divisions of the vernler scale coincide with \((\mathrm{n}-1)\) divisions of maln scale. The least count of the vernler calliper is,
- A \(\frac{1}{(n+1)(n-1)} \mathrm{cm} \)
- B \(\frac{1}{n}\; \mathrm{cm}\)
- C \(\frac{1}{n^2}\; \mathrm{cm}\)
- D \(\frac{1}{n(n+1)}\; \mathrm{cm}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{n^2}\; \mathrm{cm}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{n}(\mathrm{USD})=(\mathrm{n}-1) \mathrm{MSD} \)\(\Rightarrow 1 \mathrm{VSD}=\frac{(\mathrm{n}-1)}{\mathrm{n}} \mathrm{MSD}\) Least count \(=1 \mathrm{MSD}-1 \mathrm{VSD}=\left[1-\frac{(\mathrm{n}-1)}{\mathrm{n}}\right] \mathrm{MSD}=\frac{1}{\mathrm{n}} \mathrm{MSD}\)\(=\frac{1}{\mathrm{n}}\left(\frac{1}{\mathrm{n}}\right) \mathrm{cm}=\frac{1}{\mathrm{n}^{2}} \mathrm{cm}\)
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