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Q. In a vernier callipers, each $cm$ on the main scale is divided into $20$ equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be..... $\times 10^{-2} mm$.

JEE MainJEE Main 2022Physical World, Units and Measurements

Solution:

$20\, MSD =1\, cm$
$1\, MSD =\frac{1}{20} cm$
$10\, VSD =9\, MSD$
$1\, VSD =\frac{9}{10} MSD$
$=\frac{9}{10} \times \frac{1}{20} cm$
$1\, VSD =\frac{9}{200} cm$
$VC =1\, MSD -1 \, VSD$
$=\frac{1}{20} cm -\frac{9}{200} cm$
$=\frac{1}{200} \times 10\, mm$
$VC =5 \times 10^{-2} mm$