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1.Units, Dimensions and Measurement
hard
One main scale division of a vernier caliper is equal to $m$ units. If $n^{\text {th }}$ division of main scale coincides with $(n+1)^{\mathrm{th}}$ division of vernier scale, the least count of the vernier caliper is:
A$\frac{\mathrm{n}}{(\mathrm{n}+1)}$
B$\frac{\mathrm{m}}{(\mathrm{n}+1)}$
C$\frac{1}{(n+1)}$
D$\frac{\mathrm{m}}{\mathrm{n}(\mathrm{n}+1)}$
(JEE MAIN-2024)
Solution
$n M S D=(n+1) V S D$
$\Rightarrow 1 V S D=\frac{n}{n+1} M S D$
$L \cdot C=1 M S D-1 V S D$
$L \cdot C=m-m\left(\frac{n}{n+1}\right)$
$L \cdot C=m\left(\frac{n+1-n}{n+1}\right)$
$\Rightarrow L \cdot C=\left(\frac{m}{n+1}\right)$
$\Rightarrow 1 V S D=\frac{n}{n+1} M S D$
$L \cdot C=1 M S D-1 V S D$
$L \cdot C=m-m\left(\frac{n}{n+1}\right)$
$L \cdot C=m\left(\frac{n+1-n}{n+1}\right)$
$\Rightarrow L \cdot C=\left(\frac{m}{n+1}\right)$
Standard 11
Physics
