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 provides a measurement with fractional error given by:

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

The error in area measurement is twice the fractional error (since the error in both dimensions contributes to the total error), so:

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

Step 1: The fractional error in area will be \( \frac{4}{100} \), which means \( x = 4 \).

Final Conclusion: The value of \( x \) is 4, which corresponds to Option (2).