Diameter of a steel ball is measured using a Vernier callipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as :

If the zero error is -0.03 cm, then mean corrected diameter is :

  • Option 1)

     0.56 cm

  • Option 2)

    0.59 cm

  • Option 3)

     0.53 cm

  • Option 4)

    0.52 cm

     

 

Answers (2)

As we learnt in 

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

    

 

 

 

 

 

   M.S.D=0.1cm, VSD=9/10 MSD

                               =0.9\times 0.1= 0.09cm

Least count=MSD-VSD=0.1-0.09

                                              =0.01cm

Total reading=MS Reading \times Vernier Coincidence \times (Least count)

1st Reading=0.5\times 8\times 0.01=0.58 \:cm

2nd Reading=0.5\times 4\times 0.01=0.54 \:cm

3rd Reading=0.5\times 6\times 0.01=0.56 \:cm

Average Reading =\frac{(0.58+0.54+0.56)}{3}=0.56

Correct option is 1.


Option 1)

 0.56 cm

Correct

Option 2)

0.59 cm

Incorrect

Option 3)

 0.53 cm

Incorrect

Option 4)

0.52 cm

 

Incorrect

correct option is 2)

this prateek dude forgot to add the zero error.

 

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