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BITSAT 2024Paper 2
Exam
BITSAT
Year
2024
Paper
Paper 2
Subject
Physics
Chapter
Experimental Physics

BITSAT 2024 · Paper 2 · Physics · Experimental Physics

One main scale division of a vernier caliper is equal to m units....

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

Options

  1. An(n+1)\frac{n}{(n+1)}
  2. Bm(n+1)\frac{\mathrm{m}}{(\mathrm{n}+1)}
  3. C1(n+1)\frac{1}{(\mathrm{n}+1)}
  4. Dmn(n+1)\frac{\mathrm{m}}{\mathrm{n}(\mathrm{n}+1)}

Correct answer

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

Step-by-step solution

Given 1 Main scale division = m nMSD=(n+1)VSD⇒1VSD=nn+1MSD\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 =1MSD−1VSD⇒L.C=m−m=1 \mathrm{MSD}-1 \mathrm{VSD}\Rightarrow \quad L. C=m-m\left(\frac{n}{n+1}\right)= \llleft(1−lleft(1-\frac{n}{n+1})m=mm=m\left(\frac{n+1-n}{n+1}\right)=(1n+1)\left(\frac{1}{n+1}\right) m \Rightarrow L $cdotC=\$cdotC=\left(mn+1\frac{m}{n+1}\right)
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