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The pitch of screw gauge is $1 mm$ and there are 100 divisions on circular scale. Screw gauge is zero error free. While measuring diameter of a wire, the main scale reads $1 mm$ and $48 th$ division on circular scale coincides with the reference line. The length of wire is $5.0 cm$ . Find the volume of the wire.

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$2.6 {cm}^{3}$

$0.086 {cm}^{3}$

$0.026 {cm}^{3}$

$0.036 {cm}^{3}$

answer is B.

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Detailed Solution

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

Diameter of wire = Reading of main scale + Reading of circular scale

$= 1 mm + 48 \times LC$

$= 1 mm + 48 \times 0.01 mm$

$= 1.48 mm$

Therefore Volume of wire = $π \frac{d^{2}}{4} l$

$= 3.14 \times \frac{{(1.48 \times 10^{- 1})}^{2}}{4} \times 5 {cm}^{3}$

$= 0.0859732 {cm}^{3} = 0.086 {cm}^{3}$

$= 0.086 {cm}^{3}$

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