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1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
One main scale division of a vernier caliper is equal to $m$ units. If $n^{\text {th }}$ division of main scale coincides with $(n+1)^{\mathrm{ht}}$ division of vernier scale, the least count of the vernier caliper is:
  • A
    $\frac{\mathrm{n}}{(\mathrm{n}+1)}$
  • ✓
    $\frac{\mathrm{m}}{(\mathrm{n}+1)}$
  • C
    $\frac{1}{(n+1)}$
  • D
    $\frac{\mathrm{m}}{\mathrm{n}(\mathrm{n}+1)}$
✓

Answer

Correct option: B.
$\frac{\mathrm{m}}{(\mathrm{n}+1)}$
b
$n M S D=(n+1) V S D$

$\Rightarrow 1 V S D=\frac{n}{n+1} M S D$

$L \cdot C=1 M S D-1 V S D$

$L \cdot C=m-m\left(\frac{n}{n+1}\right)$

$L \cdot C=m\left(\frac{n+1-n}{n+1}\right)$

$\Rightarrow L \cdot C=\left(\frac{m}{n+1}\right)$

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