Question

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be \( \frac{x}{100} \), where \( x \) is:

Hint:

When dealing with measurements involving areas, remember that errors in both dimensions contribute to the total error.

Answer 1

The screw gauge yields a fractional error determined by the formula:

\[ \text{Fractional error} = \frac{\text{Smallest measurement}}{\text{Measured value}} = \frac{1}{\text{Number of divisions in the circular scale}} = \frac{1}{15} \]

The error in area measurement is double the fractional error, accounting for errors in both dimensions. Therefore:

\[ \text{Fractional error in area} = 2 \times \frac{1}{15} = \frac{2}{15} \]

Step 1: The fractional error in area is \( \frac{4}{100} \), indicating that \( x = 4 \).

Final Conclusion: The determined value for \( x \) is 4, aligning with Option (2).