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  4. The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24 text th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

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Q. The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between $5.10\, cm$ and $5.15 \,cm$ of the main scale. The Vernier scale has $50$ divisions equivalent to $2.45\, cm$. The $24^{\text {th }}$ division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

JEE AdvancedJEE Advanced 2013Physical World, Units and Measurements

Solution:

Main scale division $( s )=.05\, cm$
Vernier scale division (v) $=\frac{49}{100}=.049$
Least count $=.05-.049=.001\, cm$
Diameter: $5.10+24 \times .001$
$=5.124 \,cm$