What is the least possible error encountered when taking measurement with a meter rule?

Analysis

The question asks for the "least possible error" when using a meter rule. In physics, this is technically referred to as the uncertainty or the limit of reading accuracy of the instrument.

Concept

The limit of reading accuracy of any measuring instrument is generally taken as half of the smallest division on its scale.

1. Smallest Division: A standard meter rule is calibrated in centimeters (cm) and millimeters (mm). The smallest division on a meter rule is 1 mm (or 0.1 cm).
2. Calculation of Error: When you take a measurement, you can estimate the position of the object between the smallest markings. By convention, the smallest error (uncertainty) is half of the smallest scale division. • $\text{Error} = \frac{1}{2} \times (\text{smallest division})$ • $\text{Error} = \frac{1}{2} \times 1\text{ mm} = 0.5\text{ mm}$

Solution

• Step 1: Identify the smallest division on a meter rule, which is $1\text{ mm}$.
• Step 2: Apply the rule for reading accuracy: $\text{Uncertainty} = \frac{1}{2} \times \text{smallest division}$.
• Step 3: Calculate: $0.5 \times 1\text{ mm} = 0.5\text{ mm}$.

Therefore, the least possible error (or the limit of accuracy) when using a meter rule is $0.5\text{ mm}$.

Conclusion

The correct option is C.

Exam Tip

Always remember the "Half-Division Rule":

• Meter Rule: Smallest division = $1\text{ mm} \rightarrow$ Error = $0.5\text{ mm}$.
• Vernier Caliper: Smallest division = $0.1\text{ mm} \rightarrow$ Error = $0.05\text{ mm}$.
• Micrometer Screw Gauge: Smallest division = $0.01\text{ mm} \rightarrow$ Error = $0.005\text{ mm}$.