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Difficulty: MediumMeasurement of Length and Measuring Instruments

A Vernier caliper with a least count of 0.01 cm0.01\text{ cm} is used to measure the internal diameter of a beaker. Before making the measurement, the jaws are brought together tightly; the zero mark of the Vernier scale lies to the left of the zero mark of the main scale, and the 6th6\text{th} division on the Vernier scale coincides with a main scale division. If the observed reading for the internal diameter of the beaker is 3.43 cm3.43\text{ cm}, what is the actual internal diameter of the beaker?

  1. A
    3.39 cm3.39\text{ cm}
  2. B
    3.43 cm3.43\text{ cm}
  3. 3.47 cm3.47\text{ cm}Answer
  4. D
    3.49 cm3.49\text{ cm}

Answer

The actual internal diameter of the beaker is 3.47 cm3.47\text{ cm}.
The instrument possesses a negative zero error because the Vernier zero mark lies to the left of the main scale zero mark when closed. The magnitude of this negative error is calculated as −(10−6)×0.01 cm=−0.04 cm-(10 - 6) \times 0.01\text{ cm} = -0.04\text{ cm}. Applying the standard correction formula Actual Value=Observed Value−Zero Error\text{Actual Value} = \text{Observed Value} - \text{Zero Error} gives 3.43 cm−(−0.04 cm)=3.47 cm3.43\text{ cm} - (-0.04\text{ cm}) = 3.47\text{ cm}.

Step-by-Step Solution

1
Determine the zero error of the Vernier caliper
Zero error = −(10−6)×0.01 cm=−0.04 cm- (10 - 6) \times 0.01\text{ cm} = -0.04\text{ cm}
When the zero mark of the Vernier scale lies to the left of the main scale zero mark, the zero error is negative. For a 10-division Vernier scale, the magnitude is given by (10−N)×least count(10 - N) \times \text{least count}, where N=6N=6 is the coinciding division.
2
Apply the zero error correction formula
Actual Reading = Observed Reading - Zero Error
The true reading is obtained by subtracting the zero error (with its sign) from the observed value.
3
Calculate the actual internal diameter
Actual Diameter = 3.43 cm−(−0.04 cm)=3.47 cm3.43\text{ cm} - (-0.04\text{ cm}) = 3.47\text{ cm}
Subtracting a negative zero error is mathematically equivalent to adding its magnitude to the observed reading.

Key Concept

Vernier Caliper Zero Error Correction
Estimated Time:1m 30s
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Topics

Measurement of Length and Measuring Instruments

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