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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 cylindrical pipe. When the jaws are fully closed without any object between them, the zero mark of the Vernier scale lies to the right of the zero mark on the main scale, and the 3rd3\text{rd} Vernier division coincides with a main scale division. During measurement, the main scale reads 2.40 cm2.40\text{ cm} and the 6th6\text{th} Vernier division coincides with a main scale mark. What is the corrected internal diameter of the pipe?

  1. 2.43 cm2.43\text{ cm}Answer
  2. B
    2.46 cm2.46\text{ cm}
  3. C
    2.49 cm2.49\text{ cm}
  4. D
    2.37 cm2.37\text{ cm}

Answer

The corrected internal diameter of the pipe is 2.43 cm2.43\text{ cm}.
The Vernier caliper has a positive zero error because the zero mark on the Vernier scale lies to the right of the zero mark on the main scale when closed. The magnitude of this error is 3×0.01 cm=+0.03 cm3 \times 0.01\text{ cm} = +0.03\text{ cm}. The observed reading is 2.40 cm+(6×0.01 cm)=2.46 cm2.40\text{ cm} + (6 \times 0.01\text{ cm}) = 2.46\text{ cm}. Subtracting the zero error from the observed reading yields Corrected reading=2.46 cm−0.03 cm=2.43 cm\text{Corrected reading} = 2.46\text{ cm} - 0.03\text{ cm} = 2.43\text{ cm}.

Step-by-Step Solution

1
Determine the zero error of the Vernier caliper.
Zero error =+(3×0.01 cm)=+0.03 cm= + (3 \times 0.01\text{ cm}) = +0.03\text{ cm}.
Since the zero of the Vernier scale lies to the right of the main scale zero mark, the instrument has a positive zero error.
2
Calculate the uncorrected (observed) reading.
\text{Observed reading} = 2.40\text{ cm} + (6 \times 0.01\text{ cm}) = 2.46\text{ cm}$.
The observed reading is the sum of the main scale reading and the Vernier scale coincidence value.
3
Apply the zero error correction formula.
\text{Corrected reading} = 2.46\text{ cm} - (+0.03\text{ cm}) = 2.43\text{ cm}$.
Corrected reading is given by subtracting the zero error (including its sign) from the observed reading.

Key Concept

Zero Error Correction in Length Measurement Instruments
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Topics

Measurement of Length and Measuring Instruments

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