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- A screw gauge is commonly used to measure the thickness or diameter of a thin sheet or wire. In an experiment, a thin wire is measured using a screw gauge. The main scale reading is 3 mm, and the 1
A screw gauge is commonly used to measure the thickness or diameter of a thin sheet or wire. In an experiment, a thin wire is measured using a screw gauge. The main scale reading is 3 mm, and the 10 divisions on the circular scale coincide with one main scale division. The pitch of the screw gauge is 0.5 mm, and the zero error is −0.02 mm (i.e., the zero of the circular scale is 0.02 mm below the reference line). Calculate the diameter of the wire.
160mm
170 mm
16.04mm
20 mm
Answers (1)
Given:
Main scale reading = 3 mm
Number of circular scale divisions = 10
Pitch of screw gauge (p) = 0.5 mm
Zero error (Z.E.) = −0.02 mm
The actual reading on the circular scale (C.S.R.) is given by:
Plugging in the values:
The corrected reading is given by:
Corrected reading = C.S.R. − Z.E.
Plugging in the values:
Corrected reading = 5 mm − (−0.02 mm) = 5.02 mm
The total reading is the sum of the main scale reading and the corrected reading:
Total reading = Main scale reading + Corrected reading Plugging in the values:
Total reading = 3 mm + 5.02 mm = 8.02 mm
Since two opposite sides of the wire are measured, the diameter of the wire is twice the total reading:
Diameter = 2 × Total reading = 2 × 8.02 mm = 16.04 mm Therefore, the diameter of the wire is 16.04 mm.
Therefore, the correct option is 3.
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