The pitch of the screw gauge is $1 mm$ . There are 100 divisions on the circular scale when the gap A B is just closed, 8th division of the circular scale coincides with reference line. While measuring the diameter of a wire, the linear scale reads $1 mm$ and 50th division on the circular scale coincides with the reference line. The length of the wire is $8.6 cm$ . Find the curved surface area of the cylinder.

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$3.834 {cm}^{2}$

$2.6 {cm}^{2}$

$3.8 {cm}^{2}$

$2.68 {cm}^{2}$

answer is A.

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Detailed Solution

$LC = \frac{1}{100} = 0.01 mm$

$Zero error = + 8 \times LC$

$= 8 \times 0.01 = 0.08 mm$

Therefore Diameter of wire, d= Reading of main scale + Reading of circular scale - Zero error

d= $1 mm + 50 \times LC - 0.08 mm$

$= 1 mm + (50 \times 0.01 - 0.08) mm$

$= 1.42 mm = 1.42 \times 10^{- 1} cm$

Curved surface area = $π l d$

$= 3.14 \times 8.6 \times 1.42 \times 10^{- 1}$

$= 3.8 {cm}^{2}$

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