Q95 / 100 · BITSAT 2024 (Memory Based Paper 2) · Physics

One main scale division of a vernier caliper is equal to $m$ units. If ${m}^{\text {th }}$ division of main scale coincides with $(n+1)^{\text {th }}$ division of vernier scale, the least count of the vernier caliper is:

  • A
    $\frac{n}{(n+1)}$
  • Correct answer
    B
    $\frac{\mathrm{m}}{(\mathrm{n}+1)}$
  • C
    $\frac{1}{(\mathrm{n}+1)}$
  • D
    $\frac{\mathrm{m}}{\mathrm{n}(\mathrm{n}+1)}$

Solution

Given 1 Main scale division = m $\mathrm{n} M S D=(\mathrm{n}+1) \mathrm{VSD}$ $\Rightarrow \quad 1 \mathrm{VSD}=\frac{\mathrm{n}}{\mathrm{n}+1} \mathrm{MSD}$ Least count of vernier caliper $=1 \mathrm{MSD}-1 \mathrm{VSD}$ $\Rightarrow \quad L . C=m-m\left(\frac{n}{n+1}\right)=\left(1-\frac{n}{n+1}\right) m$ $=m\left(\frac{n+1-n}{n+1}\right)=\left(\frac{1}{n+1}\right) m \Rightarrow L \cdot C=\left(\frac{m}{n+1}\right)$

Hence, the correct answer is option: 'B'.

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