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Experimental Physics

NEET · Physics · Experimental Physics

A Vernier caliper is used to measure the diameter of a cylinder. It...

A Vernier caliper is used to measure the diameter of a cylinder. It is given that 11 main scale division (MSD) is equal to 1 mm1\text{ mm} and 2020 Vernier scale divisions (VSD) coincide with 1919 main scale divisions. While taking the measurement, the zero of the Vernier scale lies just past the 3.1 cm3.1\text{ cm} mark on the main scale, and the 14th14^{\text{th}} division of the Vernier scale coincides exactly with a main scale line. The diameter of the cylinder is:

Options

  1. A3.114 cm3.114\text{ cm}
  2. B3.24 cm3.24\text{ cm}
  3. C3.170 cm3.170\text{ cm}
  4. D4.50 cm4.50\text{ cm}

Correct answer

C. 3.170 cm3.170\text{ cm}

Step-by-step solution

Least count (LC) of the Vernier caliper is given by:
LC=1 MSD−1 VSD\text{LC} = 1\text{ MSD} - 1\text{ VSD}

Given 20 VSD=19 MSD20\text{ VSD} = 19\text{ MSD}, we have 1 VSD=1920 MSD1\text{ VSD} = \dfrac{19}{20}\text{ MSD}.
LC=1 MSD−1920 MSD=120 MSD\text{LC} = 1\text{ MSD} - \dfrac{19}{20}\text{ MSD} = \dfrac{1}{20}\text{ MSD}

Since 1 MSD=1 mm1\text{ MSD} = 1\text{ mm},
LC=120 mm=0.05 mm\text{LC} = \dfrac{1}{20}\text{ mm} = 0.05\text{ mm}

The main scale reading (MSR) is given as 3.1 cm3.1\text{ cm}, which is 31 mm31\text{ mm}.
The Vernier scale reading (VSR) is the coinciding division multiplied by the least count:
VSR=14×0.05 mm=0.70 mm\text{VSR} = 14 \times 0.05\text{ mm} = 0.70\text{ mm}

Total reading =MSR+VSR= \text{MSR} + \text{VSR}
=31 mm+0.70 mm=31.70 mm= 31\text{ mm} + 0.70\text{ mm} = 31.70\text{ mm}

Converting the final reading into cm:
Diameter =3.170 cm= 3.170\text{ cm}

Answer: 3.170 cm3.170\text{ cm}
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