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NEET
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Physics
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Experimental Physics

NEET · Physics · Experimental Physics

In a vernier caliper, 1 cm on the main scale is divided into 10...

In a vernier caliper, 1 cm1\text{ cm} on the main scale is divided into 1010 equal parts. It is given that 2020 divisions of the vernier scale coincide with 1919 divisions of the main scale. While measuring the diameter of a wire, the zero of the vernier scale lies between 2.3 cm2.3\text{ cm} and 2.4 cm2.4\text{ cm} on the main scale, and the 6th6^{\text{th}} division of the vernier scale perfectly coincides with a main scale division. The diameter of the wire is:

Options

  1. A2.36 cm2.36\text{ cm}
  2. B2.90 cm2.90\text{ cm}
  3. C2.330 cm2.330\text{ cm}
  4. D2.303 cm2.303\text{ cm}

Correct answer

C. 2.330 cm2.330\text{ cm}

Step-by-step solution

Value of one main scale division, 1 MSD=1 cm10=0.1 cm1\text{ MSD} = \dfrac{1\text{ cm}}{10} = 0.1\text{ cm}.

Given that 20 VSD=19 MSD20\text{ VSD} = 19\text{ MSD}, we have 1 VSD=1920 MSD1\text{ VSD} = \dfrac{19}{20}\text{ MSD}.

The least count (LC) of the vernier caliper is:
LC=1 MSD−1 VSD=1 MSD−1920 MSD=120 MSD\text{LC} = 1\text{ MSD} - 1\text{ VSD} = 1\text{ MSD} - \dfrac{19}{20}\text{ MSD} = \dfrac{1}{20}\text{ MSD}
LC=0.1 cm20=0.005 cm\text{LC} = \dfrac{0.1\text{ cm}}{20} = 0.005\text{ cm}

The main scale reading (MSR) is 2.3 cm2.3\text{ cm} (since the vernier zero lies between 2.32.3 and 2.4 cm2.4\text{ cm}).
The vernier scale reading (VSR) is given by the coinciding division multiplied by the least count:
VSR=6×0.005 cm=0.030 cm\text{VSR} = 6 \times 0.005\text{ cm} = 0.030\text{ cm}

Total reading = MSR+VSR=2.3 cm+0.030 cm=2.330 cm\text{MSR} + \text{VSR} = 2.3\text{ cm} + 0.030\text{ cm} = 2.330\text{ cm}.

Answer: 2.330 cm2.330\text{ cm}
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