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Units and Measurements question

2021 · 17 Mar · Shift 1 · Q57
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  5. /2021 · 17 Mar · Shift 1 · Q57

Units and Measurements question

2021 · 17 Mar · Shift 1 · Q57

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it was noted that '0' on the vernier scale lies between 8.5 cm and 8.6 cm, vernier coincidence is 6, then the correct value of measurement is ‾\underline{\hspace{2cm}}​ cm. (least count = 0.01 cm)
  1. A
    8.58 cm
  2. B
    8.54 cm
  3. C
    8.56 cm
  4. D
    8.36 cm
View written solutionFree

Correct answer: B

  1. Given data

    • Positive zero error =0.2 mm= 0.2\,\text{mm}=0.2mm
    • Least count =0.01 cm= 0.01\,\text{cm}=0.01cm
    • Main scale reading: since vernier zero lies between 8.5 cm8.5\,\text{cm}8.5cm and 8.6 cm8.6\,\text{cm}8.6cm, MSR=8.5 cm\text{MSR} = 8.5\,\text{cm}MSR=8.5cm
    • Vernier coincidence =6= 6=6
  2. Observed reading Vernier contribution is: VSR=6×0.01=0.06 cm\text{VSR} = 6 \times 0.01 = 0.06\,\text{cm}VSR=6×0.01=0.06cm

    So the observed reading is: Observed reading=8.5+0.06=8.56 cm\text{Observed reading} = 8.5 + 0.06 = 8.56\,\text{cm}Observed reading=8.5+0.06=8.56cm

  3. Zero error correction Positive zero error means the instrument reads more than the actual value. Hence correction is subtracted.

    Convert zero error into cm: 0.2 mm=0.02 cm0.2\,\text{mm} = 0.02\,\text{cm}0.2mm=0.02cm

    Therefore, Correct reading=8.56−0.02=8.54 cm\text{Correct reading} = 8.56 - 0.02 = 8.54\,\text{cm}Correct reading=8.56−0.02=8.54cm

  4. Final answer 8.54 cm\boxed{8.54\,\text{cm}}8.54cm​

  5. Option check

    • A: 8.58 cm8.58\,\text{cm}8.58cm ❌
    • B: 8.54 cm8.54\,\text{cm}8.54cm ✅
    • C: 8.56 cm8.56\,\text{cm}8.56cm ❌
    • D: 8.36 cm8.36\,\text{cm}8.36cm ❌
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