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The least count of a vernier caliper is 1/(20N) cm. One main scale division is 1 mm. The number of main scale divisions that coincide with N vernier scale divisions is

Asked in JEE Main 8th April 2nd Shift 2024 · Least count

Answer: (3) (2N-1)/2

Step-by-step solution

Let x main scale divisions coincide with N vernier divisions, so 1 VSD =x/N MSD.

L.C. =1 MSD -1 VSD =(1-x/N)×0.1 cm (since 1 MSD =0.1 cm).

Set equal to 1/(20N): 0.1(1-x/N)=1/(20N)⇒ 1-x/N=1/(2N).

x/N=(2N-1)/(2N)⇒ x=(2N-1)/2.

Why the other options are wrong

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