In a vernier callipers, <math> <mrow> <mrow> <mo>(</mo> <mrow> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </math> divisions of vernier scale coincide with <math> <mrow> <mi>N</mi> </mrow> </math> divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:

V . C = M S D − V S D … (i)given : (N+1)VSD=NMSD <!- [endif]-><!- [if gte mso 9]><xml> </xml><! [endif]-> VSD= (NN+1)MSD … (ii)From (1) and (2) V . C = ( MSD ) − N N + 1 ( MSD ) <!- [endif]-><!- [if gte mso 9]><xml> </xml><! [endif]-> =MSD (1−NN+1)=MSDN+1 <!- [endif]-><!- [if gte mso 9]><xml> </xml><! [endif]-> = 0 . 0 1 N + 1 = 1 1 0 0 ( N + 1 ) <!- [endif]-><!- [if gte mso 9]><xml> </xml><! [endif]->

In a vernier callipers, <math> <mrow> <mrow> <mo>(</mo> <mrow> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </math> divisions of vernier scale coincide with <math> <mrow> <mi>N</mi> </mrow> </math> &nbsp;divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:

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Electrostatics Physics Electrostatic Potential and Capacitance Physics Class 12th

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 -

$\frac{1}{10 N}$

Option 2 -

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

Option 3 -

100

Option 4 -

$10 (N + 1)$

4 Views | Posted 3 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

3 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)

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

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

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

<math> <mrow> <mi>V</mi> <mo>.</mo> <mi>C</mi> <mo>=</mo> <mi>M</mi> <mi>S</mi> <mi>D</mi> <mo>−</mo> <mi>V</mi> <mi>S</mi> <mi>D</mi> </mrow> </math>     … (i)given :  <math> <mrow><mrow><mo> (</mo><mrow><mi>N</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow>VSD<mo>=</mo><mi>N</mi>MSD</mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1816515870"> </o:OLEObject></xml><! [endif]-> <math> <mrow>VSD<mo>=</mo><mrow><mo> (</mo><mrow><mfrac><mrow><mi>N</mi></mrow><mrow><mi>N</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><mo>)</mo></mrow>MSD</mrow> </math>     … (ii)From (1) and (2) <math> <mrow> <mi>V</mi> <mo>.</mo> <mi>C</mi> <mo>=</mo> <mrow> <mo> (</mo> <mrow>MSD</mrow> <mo>)</mo> </mrow> <mo>−</mo> <mfrac> <mrow> <mi>N</mi> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mrow> <mo> (</mo> <mrow>MSD</mrow> <mo>)</mo> </mrow> </mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1816515872"> </o:OLEObject></xml><! [endif]-> <math> <mrow><mo>=</mo>MSD<mrow><mo> (</mo><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><mi>N</mi></mrow><mrow><mi>N</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><mo>)</mo></mrow><mo>=</mo><mfrac><mrow>MSD</mrow><mrow><mi>N</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1816515873"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>0</mn> <mo>.</mo> <mn>0</mn> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mo>=</mo> <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> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1030" DrawAspect="Content" ObjectID="_1816515874"> </o:OLEObject></xml><! [endif]->