Metre rule and measuring tape: three readings, one right answer

The problem

In Fig. 1.1 (p. 12) one object lies on a ruler. Read from the left you get 1.5 cm, from straight above 1.8 cm, from the right 2.0 cm. Same object, same ruler. Which reading do you write?

In the lab, length is usually measured with a metre rule. Its smallest division is 1 mm, so the smallest length it can measure accurately is 1 mm. That is its least count.

Place the rule so its zero lines up with one edge of the object, then read the mark at the other edge. A measuring tape works the same way for longer distances, also with a least count of 1 mm.

Reading from an angle makes the object seem a different length. This is parallax error. Keep your eye directly above the mark, perpendicular to the scale, or tip the rule on its edge.

Least count is the smallest measurement an instrument can take accurately: 1 mm for a metre rule or tape. Read with your eye directly above the mark, or parallax changes the reading.

Key terms

Least count

The smallest measurement an instrument can take accurately.

Metre rule

The usual lab scale for lengths from 1 mm to 1 m.

Measuring tape

Longer distances, still with a least count of 1 mm.

Parallax error

The change in a reading caused by looking at the scale from an angle.

Short questions with model answers

1. Q1. Which instrument should measure the length of a football ground, 9.1 × 10¹ m?

   • 9.1 × 10¹ m = 91 m
   • A metre rule only reaches 1 m; a tape reaches several metres.

   A measuring tape.

2. Q2. Can a metre rule give the diameter of a pencil, 7.0 × 10⁻³ m, to a tenth of a millimetre?

   • 7.0 × 10⁻³ m = 7.0 mm
   • The metre rule's least count is 1 mm.

   No; you need an instrument with a smaller least count (next lesson).

3. Q3. Activity 1.2 (p. 14): how does a metre rule give the thickness of one coin?

   • Stack ten coins and measure the total height.
   • one coin = total height ÷ 10

   Measure ten together, then divide by 10.

Common mistakes

• ✗ Reading the scale from the side.

  ✓ Put your eye directly above the mark, perpendicular to the scale.

• ✗ Starting from the worn end of the rule instead of a clear mark.

  ✓ Line one edge up with a clear mark and subtract that mark from the reading at the other edge.

• ✗ Thinking the least count is the length of the whole rule.

  ✓ It is the smallest division you can read accurately: 1 mm on a metre rule.

MCQs

1. 1. The least count of a metre rule is:

   1. (a) 1 cm
   2. (b) 0.1 mm
   3. (c) 1 mm
   4. (d) 1 m
   Show answer

   (c) Its smallest division is 1 mm (p. 11).

2. 2. Parallax error is due to:

   1. (a) Incorrect position of the eye
   2. (b) A worn-out rule
   3. (c) A hot room
   4. (d) A long object
   Show answer

   (a) Your book's For Your Information box (p. 12).

3. 3. Short Q 1.11 (p. 25): in Fig. 1.1, which position gives the correct length?

   1. (a) A, 1.5 cm
   2. (b) B, 1.8 cm
   3. (c) C, 2.0 cm
   4. (d) All three
   Show answer

   (b) At B the eye is directly above the mark, so there is no parallax.

4. 4. The range of a metre rule is:

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

   (d) Limitations table, p. 15.

5. 5. A measuring tape is chosen over a metre rule when:

   1. (a) The length is less than 1 mm
   2. (b) A smaller least count is needed
   3. (c) The distance is several metres
   4. (d) The object is hot
   Show answer

   (c) Both have a 1 mm least count; the tape simply reaches longer distances.

Quick revision

• Least count is the smallest accurate reading: 1 mm for a metre rule and a tape.
• Zero at one edge, read at the other, eye directly above: no parallax.
• Choose by range: rule up to 1 m, tape for several metres.