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Solve this problem In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25 cm. There are 100 circular scaledivisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale division

In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25 cm. There are 100 circular scale
divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is :

  • Option 1)

    0.4300 cm

  • Option 2)

    0.2150 cm

  • Option 3)

    0.3150 cm

  • Option 4)

    0.0430 cm

 
Answers (2)
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As we learned

 

To measure the diameter of small spherical cylindrical body using Vernier Callipers -

Vernier Constant

= 1 Main scale division - 1 V.S. Division 

V.C= 1 M.S.D - 1 V.S.D

M.S.D=  Main Scale Reading

V.S.D= Vernier Scale Reading

 

- wherein

Total observed reading = N+n \times V.C

N= Nth division 

Observations: 

1.    Vernier constant (least count) of the Vernier Callipers: 

                    1 M.S.D. = 1 mm

            10 vernier scale divisions = 9 main scale divisions

                i.e.     10 V.S.D. = 9 M.S.D.

    \therefore        1 V.S.D. = =\frac{9}{10} M.S.D.

                Vernier Constant (L.C.) = 1 M.S.D. - 1 V.S.D. = 1 M.S.D. -\frac{9}{10} M.S.D.

                            =\left(1-\frac{9}{10} \right )M.S.D.=\frac{1}{10}\times1M.S.D.

                            =\frac{1}{10}\times1mm=0.1mm=0.01cm

2.    Zero error: (i) ........ cm (ii) ............cm (iii) ..........cm 

        Mean Zero Error (e) = ............ cm 

        Mean Zero Correction (c) = - (Mean Zero Error)

                                                = .......... cm

    

 

 

 

 

 

   least count =\frac{0.25}{5\times 100}cm = 5\times 10^{-4}cm

 

Reading = 4\times 0.05 cm +30\times 5\times 10^{-4}cm

=(0.2+0.0150)cm

= 0.2150cm


Option 1)

0.4300 cm

Option 2)

0.2150 cm

Option 3)

0.3150 cm

Option 4)

0.0430 cm

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