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  4. A travelling microscope has 20 divisions per cm on the main scale while its Vernier scale has total 50 divisions and 25 Vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope ?

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Q. A travelling microscope has $20$ divisions per $cm$ on the main scale while its Vernier scale has total $50 $ divisions and $25$ Vernier scale divisions are equal to $24$ main scale divisions, what is the least count of the travelling microscope ?

JEE MainJEE Main 2022Physical World, Units and Measurements

Solution:

$ 1 MSD =\frac{1}{20} cm $
$1 VSD =\frac{24}{25} MSD =\frac{24}{25} \times \frac{1}{20} cm$
$ \therefore \text { Least count }=\frac{1}{20}\left(1-\frac{24}{25}\right) cm $
$=\frac{1}{20} \times \frac{1}{25}=\frac{1}{500} cm $
$ =0.002\, cm$