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 $\frac{1}{n(n+1)}\; \mathrm{cm}$
NEET 2019, Diffcult
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C $\frac{1}{n^2}\; \mathrm{cm}$
c $\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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