In a vernier callipers, $(N + 1)$ divisions of vernier scale coincide with $N$ divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:

Option 1 - <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow><mn>1</mn><mn>0</mn> N</mrow> </mfrac> </mrow> </math>

Option 2 - <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mn>0</mn> <mrow> <mo>(</mo> <mrow> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </math>

Option 3 - 100

Option 4 - <math> <mrow> <mn>1</mn> <mn>0</mn> <mrow> <mo>(</mo> <mrow> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </math>

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Answered by

Alok Kumar Singh | Contributor-Level 10

6 months ago

Correct Option - 2

Detailed Solution:

$V . C = M S D - V S D$ … (i)

given : $(N + 1) VSD = N MSD$

$VSD = (\frac{N}{N + 1}) MSD$ … (ii)

From (1) and (2)

$V . C = (MSD) - \frac{N}{N + 1} (MSD)$

$= MSD (1 - \frac{N}{N + 1}) = \frac{MSD}{N + 1}$

$= \frac{0.01}{N + 1} = \frac{1}{100 (N + 1)}$

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In a vernier callipers, ( N + 1 ) divisions of vernier scale coincide with N divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:

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