Micrometer screw gauge: measuring a hundredth of a millimetre

The problem

A page of this book is about 1.0 × 10⁻⁴ m thick, just 0.1 mm. That is the whole least count of the Vernier Callipers. For a wire or a metal sheet, you need something finer.

The micrometer screw gauge has a main scale on the sleeve, marked every 0.5 mm, and a circular scale on the thimble with 50 divisions. One full turn of the thimble moves the spindle 0.5 mm. This distance is the pitch.

So one circular division moves the spindle 0.5 mm ÷ 50 = 0.01 mm. That is the least count. The object sits between the anvil and the spindle, and the ratchet clicks to stop you over-tightening.

Close the anvil and spindle first. Circular zero on the horizontal line: no zero error. Below the line: it reads more, so subtract. Above the line: it reads less, so add.

Least count = pitch ÷ number of circular divisions = 0.5 mm ÷ 50 = 0.01 mm. Reading = main scale reading + circular scale reading × least count.

Key terms

Pitch

The distance the spindle moves in one complete turn of the thimble.

Circular scale

The scale on the thimble; the division on the line gives the hundredths.

Least count (screw gauge)

Pitch divided by the number of circular divisions.

Ratchet

Stops over-tightening; it clicks when the gauge is ready to read.

Short questions with model answers

1. Q1. Activity 1.3 (p. 16): why measure 100 sheets of the textbook and divide by 100?

   • 100 × 0.1 mm = 10 mm
   • Divide the reading by 100 to estimate one sheet.

   A thick stack reads well; dividing spreads the error over 100 sheets.

2. Q2. The circular zero is below the horizontal line when the anvil and spindle touch. What do you do?

   • Below the line, the gauge reads slightly more.
   • Subtract the zero error from every reading.

   Subtract the zero error.

Common mistakes

• ✗ Calling the pitch (0.5 mm) the least count.

  ✓ Least count = pitch ÷ circular divisions = 0.01 mm.

• ✗ Adding the circular reading as millimetres: 6.5 mm + 25 mm.

  ✓ Multiply it by the least count first: 25 × 0.01 mm = 0.25 mm.

• ✗ Adding the zero error when the circular zero is below the line.

  ✓ Below the line it reads more, so subtract; above the line, add.

MCQs

1. 1. The least count of the screw gauge in your book is:

   1. (a) 0.5 mm
   2. (b) 0.1 mm
   3. (c) 0.05 mm
   4. (d) 0.01 mm
   Show answer

   (d) 0.5 mm ÷ 50 = 0.01 mm.

2. 2. The ratchet of a screw gauge:

   1. (a) Prevents over-tightening
   2. (b) Measures depth
   3. (c) Holds the circular scale
   4. (d) Sets the pitch
   Show answer

   (a) It clicks when the gauge is ready to read (Fig. 1.5).

3. 3. Sleeve 6.5 mm, circular division 25. The thickness is:

   1. (a) 31.5 mm
   2. (b) 6.75 mm
   3. (c) 6.525 mm
   4. (d) 9.0 mm
   Show answer

   (b) 6.5 + 25 × 0.01 = 6.75 mm (Fig. 1.7).

4. 4. The range of a micrometer screw gauge is:

   1. (a) 1 mm to 1 m
   2. (b) 0.1 mm to 15 cm
   3. (c) 0.01 mm to 2.5 cm
   4. (d) 1 cm to several metres
   Show answer

   (c) Limitations table, p. 15.

5. 5. The circular zero is above the horizontal line with the jaws closed. The zero error is:

   1. (a) Subtracted
   2. (b) Ignored
   3. (c) Added
   4. (d) Doubled
   Show answer

   (c) Above the line it reads less than the true thickness, so add (p. 15).

Quick revision

• Pitch 0.5 mm, 50 circular divisions: least count 0.01 mm.
• Reading = sleeve reading + circular reading × least count: 6.75 mm in Fig. 1.7.
• Pick by range and least count: tape, rule, callipers, screw gauge.