Question

When the screw and stud touch each other, the edges of a certain screw gauge is on left of the \(\mathrm{O}\) mark on the main scale and the \(96^{\text {th }}\) division of the circular scale coincides with the circular line of graduation then what is the value of zero error? (A) zero error \(=+0.96 \mathrm{~mm}\) (B) zero error \(=-0.96 \mathrm{~mm}\) (C) zero error \(=+0.04 \mathrm{~mm}\) (D) zero error \(=-0.04 \mathrm{~mm}\)

Short answer

The zero error is positive, and its value is +0.96 mm.

Step-by-step solution

Identify the type of zero error

To determine whether the zero error is positive or negative, we observe the location of the O mark on the main scale when the screw gauge is closed without any object. In this problem, the O mark is on the left side of the circular graduation line, meaning that the reading is greater than zero. This indicates a positive zero error.

Calculate the positive zero error value

We know that the 96th division on the circular scale coincides with the circular graduation line. To calculate the zero error value, we need to multiply the 96 divisions by the least count of the screw gauge. The least count (LC) of a screw gauge can be calculated as follows: LC = pitch / number of divisions on circular scale In this problem, the pitch and number of divisions on the circular scale are not given. However, we can deduce that the least count is 0.01 mm because it is a standard in most screw gauge problems. So, the zero error value can be calculated as: Zero error value = positive zero error × least count = 96 divisions × 0.01 mm/division = 0.96 mm This means the correct answer is: (A) zero error = +0.96 mm

Key concepts

screw gauge calibration

Screw gauge calibration is essential in ensuring accurate measurements. Calibration of a screw gauge involves checking and adjusting the device to align precision and accuracy standards. This helps in maintaining the reliability of the measurements obtained from the device.
To calibrate a screw gauge, follow these main steps:

• Inspect the device for any physical damage or wear that could affect measurements.
• Close the screw gauge completely and check whether the zero mark on the main scale aligns with the zero on the circular scale. This is crucial as it ensures that the device reads zero when closed.
• Adjust accordingly if there are any misalignments, which indicates zero error. This adjustment may be done by recalibrating the zero point or using correction factors during measurement interpretation.

Regular calibration is important as it not only prevents measurement errors but also prolongs the lifespan of the screw gauge.

measurement error

Measurement errors occur when there's a discrepancy between the measured value and the true value. In the context of a screw gauge, such errors arise due to imperfections in the gauge, user handling errors, or environmental factors.
Common Types of Measurement Errors in Screw Gauge Application:

• **Zero Error**: Happens when the measuring instrument does not read zero when the object to be measured is absent.
• **Parallelism Error**: Occurs when the spindle and the object are not parallel during measurement.
• **Random Errors**: These errors are unpredictable and include fluctuating readings caused by atmospheric variations.

To minimize measurement errors, ensure the screw gauge is thoroughly checked for zero error and align the object properly with the scales during measurement. Also, handle the gauge carefully and maintain optimal conditions for measurement.

least count calculation

The least count of a screw gauge is the smallest measurable value that the gauge can accurately determine. It is a vital parameter as it determines the precision of the screw gauge.
The formula for the least count calculation is:
\[\text{Least Count (LC)} = \frac{\text{Pitch}}{\text{Number of Divisions on the Circular Scale}}\]
Where the pitch is the distance moved by the screw in one complete rotation.
In most standard screw gauges, the least count is 0.01 mm, meaning the scale can measure changes as small as this value.
This calculation helps users understand how finely a measurement can be taken using a particular screw gauge. Knowing the least count is essential, especially in precise measurements required in experiments or industrial applications.