The main scale of a vemier callipers reads $10 mm$ in 10 divisions. Ten divisions of vemier scale coincide with nine divisions of the main scale. When the two jaws of the callipers touch each other, the fifth division of the vernier coincides with 9 main scale divisions and the zero of the vernier is to the right of zero of main scale, when a cylinder is tightly placed between the two jaws. the zero of the vernier scale lies slightly to the right of $3.2 cm$ and the fourth vernier division coincides with a main scale division. Find diameter of the cylinder.

Moderate

Solution

$L = \frac{Smallest division on main scale}{Number of divisions on vernier scale}$
$= \frac{1 mm}{10} = 0.1 mm = 0.01 cm$
positive zero error $= N + x (LC)$
$= 0 + 5 \times 0.01$
$= 0.05 cm$
Diameter $= 3.2 + 4 \times 0.01 = 3.24 cm$
Actual diameter $= 3.24 - 0.05 = 3.19 cm$

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