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  4. The length is measured using a vernier system whose main scale is 30 cm long with 600 divisions. If 19 divisions of the main scale coincide with 20 divisions of the vernier scale, then its least count is

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Q. The length is measured using a vernier system whose main scale is $30\, cm$ long with $600$ divisions. If $19$ divisions of the main scale coincide with $20$ divisions of the vernier scale, then its least count is

KEAMKEAM 2018Physical World, Units and Measurements

Solution:

$\because$ Least count $=M S D-V S D$
$\because MSD =\frac{\left(\frac{30}{100}\right)}{600}=5 \times 10^{-4}\, m$
and $VSD =\frac{19}{20} \times MSD$
$=\frac{19}{20} \times 5 \times 10^{-4}=4.75 \times 10^{-4}$
$\therefore $ Least count $=(5-4.75) \times 10^{-4}=0.025\, mm$