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  4. Smallest division on the main scale of given vernier calipers is 0.5 mm. Vernier scale has 25 divisions and these coincide with 24 main scale divisions. The least count of vernier calipers is

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Q. Smallest division on the main scale of given vernier calipers is $0.5\,mm$. Vernier scale has $25$ divisions and these coincide with $24$ main scale divisions. The least count of vernier calipers is

J & K CETJ & K CET 2015Physical World, Units and Measurements

Solution:

Least count of vernier calliper $L C=1\, M S D-1\, V S D$
where, $M S D=$ Main Scale Division VSD = Vernier Scale Division
$=0.5\, mm -\frac{24}{25} M S D$
$=0.5\, mm -\frac{24}{25} \times 0.5\, mm$
$=0.5\, m \left(1-\frac{24}{25}\right)=0.5\, mm \times \frac{1}{25}$
$=\frac{1}{50} mm =0.02\, mm =0.002\, cm$