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

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

(a) 3.32 mm

(b) 3.73 mm

(c) 3.67 mm

(d) 3.38 mm

Sol: Pitch of screw gauge = 1/2 mm = 0.5 mm

Least count of screw gauge = 0.5/50 mm = 0.01 mm

Zero error = – 0.03 mm

Zero correction = + 0.03 mm

Observed diameter of wire = 3 mm + 35 x 0.01 mm = 3.35 mm

Corrected diameter of wire = (3.35 + 0.03 ) mm = 3.38 mm