Question

A student measured the diameter of a small steel ball using a screw gauge of least count $0.001\, cm$. The main scale reading is $5\, mm$ and zero of circular scale division coincides with $25$ divisions above the reference level. If screw gauge has a zero error of - $0.004\, cm$, the correct diameter of the ball is

• A. 0.529 cm
• B. 0.521 cm
• C. 0.053 cm
• D. 0.525 cm

Answer 1

The Correct Option is A

To find the correct diameter of the small steel ball, we must follow these steps using a screw gauge:

1. Understand the measurements given:
   • Main scale reading (MSR): 5 \, \text{mm} = 0.5 \, \text{cm}
   • Circular scale division (CSD) that coincides: 25
   • Least count of the screw gauge: 0.001 \, \text{cm}
   • Zero error: -0.004 \, \text{cm}
2. Calculate the circular scale reading (CSR):
   • CSR = Circular scale division × Least count
   • CSR = 25 \times 0.001 \, \text{cm} = 0.025 \, \text{cm}
3. Find the observed diameter of the ball:
   • Observed diameter = MSR + CSR
   • = 0.5 \, \text{cm} + 0.025 \, \text{cm} = 0.525 \, \text{cm}
4. Apply the zero error correction:
   • Corrected diameter = Observed diameter - Zero error
   • = 0.525 \, \text{cm} - (-0.004 \, \text{cm}) = 0.525 \, \text{cm} + 0.004 \, \text{cm} = 0.529 \, \text{cm}

Therefore, the correct diameter of the steel ball is 0.529 \, \text{cm}, and the answer is 0.529 cm.

This problem demonstrates how essential it is to account for zero error in precision instruments like screw gauges to ensure accurate measurements.