A screw gauge of pitch 0.5 mm is used to measure the diameter of uniform wire of length 6.8 cm, the main scale reading is 1.5 mm and circular scale reading is 7. The calculated curved surface area of wire to appropriate significant figures is :
[Screw gauge has 50 divisions on its circular scale]

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2.4 cm²

3.9 cm²

6.8 cm²

3.4 cm²

answer is B.

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Detailed Solution

Least count $= \frac{0.5}{50} mm = 0.01 mm$
$∴ Diameter, d = 1 .5 mm + 7 \times 0 .01$
= 1.57 mm
$∴$ Surface area $= (2 π r) \times l$
$\begin{array}{l} = πdl \\ = 3 .142 \times \frac{1 .57}{10} \times 6 .8 {cm}^{2} \\ = 3 .354 {cm}^{2} = 3 .4 {cm}^{2} \end{array}$