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NEET
Exam
NEET
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Physics
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Experimental Physics

NEET · Physics · Experimental Physics

The main scale of a vernier calipers has divisions of length a . It...

The main scale of a vernier calipers has divisions of length aa. It is found that nn divisions of the vernier scale coincide with (n−2)(n-2) divisions of the main scale. The least count of the vernier calipers is :

Options

  1. Aan\dfrac{a}{n}
  2. B2an\dfrac{2a}{n}
  3. C(n−2)an\dfrac{(n-2)a}{n}
  4. Dan−2\dfrac{a}{n-2}

Correct answer

B. 2an\dfrac{2a}{n}

Step-by-step solution

Given n VSD=(n−2) MSDn\text{ VSD} = (n-2)\text{ MSD}.

1 VSD=n−2n MSD1\text{ VSD} = \dfrac{n-2}{n}\text{ MSD}.

The least count is given by 1 MSD−1 VSD1\text{ MSD} - 1\text{ VSD}.

Least count =1 MSD−n−2n MSD= 1\text{ MSD} - \dfrac{n-2}{n}\text{ MSD}

Least count =(1−n−2n) MSD=(n−n+2n) MSD=2n MSD= \left(1 - \dfrac{n-2}{n}\right)\text{ MSD} = \left(\dfrac{n - n + 2}{n}\right)\text{ MSD} = \dfrac{2}{n}\text{ MSD}.

Since 1 MSD=a1\text{ MSD} = a, the least count is 2an\dfrac{2a}{n}.

Answer: 2an\dfrac{2a}{n}
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