Question

Diameter of a steel ball is measured using a Vernier caliper 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 (1) MSR = 0:5 cm, VSD = 8 (2)

MSR = 0:5 cm, VSD = 4 (3) MSR = 0:5 cm, VSD = 6. If the zero error is 0:03 cm, then mean

corrected diameter is

1. 0.53cm
2. 0.56cm
3. 0.59cm
4. 0.52cm

Please elaborate​

Answer 1

(There are some errors in the question. All the semicolons in the questions are to be replaced by the decimal points. And, the Zero error is -0.03 cm)

We have,

Main Scale Division (MSD) = 0.1 cm

∵ 10 divisions of its Vernier scale (VS) match 9 divisions  on the main scale,

∴ Vernier Scale Division (VSD) = $\frac{9}{10}$ × MSD = $\frac{9}{10}$ × 0.1 cm = 0.09 cm

Then,

Least Count = MSD - VSD = (0.1 - 0.09 cm) = 0.01 cm

Now, Total Reading = Main Scale Reading × Vernier Scale Reading × Least Count

∴ $R_1$ = (0.5 × 8 × 0.01) cm = 0.58 cm

$R _2$ = (0.5 × 4 × 0.01) cm = 0.54 cm

$R_3$ = (0.5 × 6 × 0.01) cm = 0.56 cm

Taking the average of all the three readings above;

$\frac{R_1 + R_2 + R_3 }{3}$ cm = $\frac{1.68}{3}$ cm= 0.56 cm

∴ Mean corrected diameter = Reading + Zero error = 0.56 - (-0.03) = 0.59 cm

Ans) (3) 0.59 cm

Answer 2

Answer:

Correct option is

3) 0.59

Explanation:

Given:

Diameter of the ball = 0.1 cm

10VSD = 9 MSD

zero error = 0.03cm

Now, LC = MSD ( 1 - Number of MSD/Number of VSD)

              = 0.1 ( 1 - 9/10)

              = 0.01cm

Case (1)

Where MSR = 0.5 cm and VSD = 8

CR = TR - error = MSR + L.C.×VSD−error

                         = 0.5 cm+0.01×8−(−0.03) cm =0.61 cm

Case (2)

Where MSR = 0.5 cm and VSD = 4

CR = TR - error = MSR + L.C.×VSD−error

                         = 0.5 cm+0.01×4−(−0.03) cm =0.57 cm

Case (3)

Where MSR = 0.5 cm and VSD = 6

CR = TR - error = MSR + L.C.×VSD−error

                         = 0.5 cm+0.01×6−(−0.03) cm =0.59 cm

Taking average of three readings diameter = (0.61+0.57+0.59)/3 = =0.59 cm

CR = Correct reading

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