JEE Challenger
More from Units and Measurements
PhyEasyAdv 2010 • Paper 2

Calculate Least Count of Vernier Calipers with Given Division Ratio

A Vernier calipers has 1 mm1\text{ mm} marks on the main scale. It has 2020 equal divisions on the Vernier scale which match with 1616 main scale divisions. For this Vernier calipers, the least count is

Options

A

0.02 mm0.02\text{ mm}

B

0.05 mm0.05\text{ mm}

C

0.1 mm0.1\text{ mm}

D

0.2 mm0.2\text{ mm}

Correct

Topics & Concepts

Units and MeasurementsMeasuring Instruments

Step-by-Step Solution

To find the least count (LC\text{LC}) of the given Vernier calipers, we use the formula:
LC=1 MSD−1 VSD\text{LC} = 1\text{ MSD} - 1\text{ VSD}

where MSD\text{MSD} represents the value of one main scale division and VSD\text{VSD} represents the value of one Vernier scale division.

Given:

  1. Value of 1 MSD=1 mm1\text{ MSD} = 1\text{ mm}
  2. 2020 Vernier scale divisions coincide with 1616 main scale divisions:
    20 VSD=16 MSD20\text{ VSD} = 16\text{ MSD}

From this, we can calculate the value of 1 VSD1\text{ VSD}:
1 VSD=1620 MSD=45 MSD=0.8 MSD1\text{ VSD} = \frac{16}{20}\text{ MSD} = \frac{4}{5}\text{ MSD} = 0.8\text{ MSD}

Since 1 MSD=1 mm1\text{ MSD} = 1\text{ mm}, we have:
1 VSD=0.8×1 mm=0.8 mm1\text{ VSD} = 0.8 \times 1\text{ mm} = 0.8\text{ mm}

Now, calculating the least count:
LC=1 MSD−1 VSD=1 mm−0.8 mm=0.2 mm\text{LC} = 1\text{ MSD} - 1\text{ VSD} = 1\text{ mm} - 0.8\text{ mm} = 0.2\text{ mm}

Thus, the least count of the Vernier calipers is 0.2 mm0.2\text{ mm}, which corresponds to Option D.

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