Q.

A screw gauge of pitch 1mm has a circular scale divided into 100 divisions and has no zero error.  When the diameter of a wire is measured using this screw gauge, the main scale reading is 1 mm and the 47th circular division coincides with the main scale.  The length of the wire is given as 5.6 cm.  The curved surface area of the wire up to the correct significant figures is

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a

25.9 cm2

b

0.259 cm2

c

2.59 cm2

d

2.6 cm2

answer is D.

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Detailed Solution

Least count of screw gauge = Pitch of the screwNo.of circular scale dvisions=1100=0.01mm diameter=MSR+LC(CSR) d=(1+0.01×47)mm = 1.47mm = 0.147 cmA=πld=227×0.147×5.6≈2.6cm2(to two significant figures)
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A screw gauge of pitch 1mm has a circular scale divided into 100 divisions and has no zero error.  When the diameter of a wire is measured using this screw gauge, the main scale reading is 1 mm and the 47th circular division coincides with the main scale.  The length of the wire is given as 5.6 cm.  The curved surface area of the wire up to the correct significant figures is