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Home » The main scale of a vernier callipers has divisions/cm. divisions of the vernier scale coincide with divisions of main scale. The least count of the vernier callipers is, (1) (2) (3) (4)
The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (\mathrm{n}-1) divisions of main scale. The least count of the vernier callipers is, (1) \frac{1}{n(n+1)} \mathrm{cm} (2) \frac{1}{(n+1)(n-1)} c m (3) \frac{1}{n} \mathrm{~cm} (4) \frac{1}{n^{2}} \mathrm{~cm}
Physics | Physics
The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (\mathrm{n}-1) divisions of main scale. The least count of the vernier callipers is, (1) \frac{1}{n(n+1)} \mathrm{cm} (2) \frac{1}{(n+1)(n-1)} c m (3) \frac{1}{n} \mathrm{~cm} (4) \frac{1}{n^{2}} \mathrm{~cm}

Answer (4)
Sol. n V S D=(n-1) MSD
1 \mathrm{VSD}=\frac{(\mathrm{n}-1)}{\mathrm{n}} \mathrm{MSD}

\begin{aligned} \text { L.C. } &=1 \mathrm{MSD}-1 \mathrm{VSD} \\ &=1 \mathrm{MSD}-\frac{(\mathrm{n}-1)}{\mathrm{n}} \mathrm{MSD} \\ &=\frac{1}{\mathrm{n}} \mathrm{MSD} \\ &=\frac{1}{\mathrm{n}} \times \frac{1}{\mathrm{n}} \mathrm{cm} \\ &=\frac{1}{\mathrm{n}^{2}} \mathrm{~cm} \end{aligned}

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