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

Answer 1

The Correct Option is A

To determine the correct diameter of the steel ball using a screw gauge, we'll follow these steps:

1. Initial Measurement:
   • Main Scale Reading (MSR) = 5 mm = 0.5 cm (since 1 mm = 0.1 cm)
   • Circular Scale Reading (CSR) = 25 divisions
2. Least Count of Screw Gauge:
   • The least count is 0.001 cm.
3. Calculating the Total Reading: \text{Total Reading (TR) = MSR + (CSR \times \text{Least Count})}
   • \text{TR} = 0.5 \, \text{cm} + (25 \times 0.001 \, \text{cm}) = 0.5 \, \text{cm} + 0.025 \, \text{cm} = 0.525 \, \text{cm}
4. Zero Error Correction:
   • The zero error is given as -0.004 cm, which means the gauge reads 0.004 cm more than the actual measurement.
   • Corrected Diameter = Total Reading - Zero Error
   • \text{Corrected Diameter} = 0.525 \, \text{cm} - (-0.004 \, \text{cm}) = 0.525 \, \text{cm} + 0.004 \, \text{cm} = 0.521 \, \text{cm}

Therefore, the correct diameter of the ball is 0.521 cm. This matches the provided correct answer.