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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.

Option: 1

160mm


Option: 2

170 mm


Option: 3

16.04mm


Option: 4

20 mm


Answers (1)

best_answer

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:

\text { C.S.R. }=\frac{\text { Number of circular scale divisions }}{\text { Number of main scale divisions }} \times \text { Pitch }

Plugging in the values:

\text { C.S.R. }=\frac{10}{1} \times 0.5 \mathrm{~mm}=5 \mathrm{~mm}

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.

Posted by

shivangi.shekhar

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