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JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement

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 _______.

  1. A \(\frac{\mathrm{n}}{(\mathrm{n}+1)}\)
  2. B \(\frac{\mathrm{m}}{(\mathrm{n}+1)}\)
  3. C \(\frac{1}{(n+1)}\)
  4. D \(\frac{\mathrm{m}}{\mathrm{n}(\mathrm{n}+1)}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\mathrm{m}}{(\mathrm{n}+1)}\)

Step-by-step Solution

Detailed explanation

\(n M S D=(n+1) V S D\) \(\Rightarrow 1 V S D=\frac{n}{n+1} M S D\) \(L \cdot C=1 M S D-1 V S D\) \(L \cdot C=m-m\left(\frac{n}{n+1}\right)\) \(L \cdot C=m\left(\frac{n+1-n}{n+1}\right)\) \(\Rightarrow L \cdot C=\left(\frac{m}{n+1}\right)\)