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Q.

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of −0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

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a

3.32 mm

b

3.73 mm

c

3.67 mm

d

3.38 mm

answer is D.

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Detailed Solution

pitch of the screw=distance travelled by the screwNo. of complete rotations made=1mm2=0.5mm LC=Pitch of the screw N0. of CSDS=0.5mm50 diameter=M.S.R+C.S.R×L.C+Z.E=3+35×(0.5/50)+0.03=3.38  mm
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Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of −0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is