Question

In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is_______ mm. [Assume least count is 0.01 mm]}

Hint:

"Zero above, you must add. Zero below, you must subtract." This is the easiest way to remember how to correct for zero errors in a screw gauge.

Answer 1

Correct Answer: 2

Step 1: Understanding the Concept:
When the zero of the circular scale is \textit{above} the reference line during contact, it indicates a negative zero error. The instrument effectively starts "behind" zero, so the actual reading is smaller than the true value. Therefore, we must \textit{add} the error magnitude to the observed reading.

Step 2: Key Formula or Approach:
1. Measured Value = PSR + (CSR $\times$ LC).
2. Correct Reading = Measured Value $-$ Zero Error (with sign).
3. Negative Zero Error = $-(n \times LC)$.
Step 3: Detailed Explanation:
Given: Least Count (LC) = 0.01 mm.
Zero Error: 3 divisions above the line $\implies$ Zero Error $= -3 \times 0.01 = -0.03$ mm.
Measured Value: PSR = 1 mm. CSR = 51. Measured Value $= 1 + (51 \times 0.01) = 1 + 0.51 = 1.51$ mm.
Correct Thickness $= \text{Measured Value} - \text{Zero Error}$ Correct Thickness $= 1.51 - (-0.03) = 1.51 + 0.03 = 1.54$ mm.
Step 4: Final Answer:
The correct thickness of the sheet is 1.54 mm.