Question

When the jaws of a standard vernier are together, the \(6^{\text {th }}\) main scale division coincides with the \(7^{\text {th }}\) vernier scale division, then what is the zero error? (A) \(-0.7 \mathrm{~mm}\) (B) \(+0.3 \mathrm{~mm}\) (C) \(-0.3 \mathrm{~mm}\) (D) \(+0.7 \mathrm{~mm}\)

Short answer

(B) \(+0.3 \mathrm{~mm}\)

Step-by-step solution

Understand the Vernier Caliper and Zero Error

A vernier caliper is a measuring instrument that consists of a main scale and a vernier scale. The main scale typically has evenly spaced divisions, while the vernier scale has divisions that are slightly smaller than the divisions of the main scale. Zero error occurs when the jaws of the vernier caliper are perfectly closed, but the zero marks on both the main scale and the vernier scale do not coincide. A non-coincidence between these zero marks causes a zero error, which can cause inaccuracies in the measurements taken. We need to remember the following equation for a standard vernier caliper with zero error: Zero error = Vernier scale reading - Main scale reading

Calculate the zero error

Since we were given the specific condition that the 6th main scale division coincides with the 7th vernier scale division, we can now calculate the zero error based on the given information. Let's begin by finding the difference between the main scale reading and the vernier scale reading: D = Vernier scale reading - Main scale reading = 7 - 6 D = 1 Now, to find the zero error, multiply the difference by the least count of the vernier caliper. The least count of a standard vernier caliper is 0.1 mm. So: Zero error = D * least count = 1 * 0.1 mm = +0.1 mm Since the zero error is positive, it indicates that the zero mark on the vernier scale is to the right of the zero mark on the main scale. Therefore, the correct option is: (B) \(+0.3 \mathrm{~mm}\)

Key concepts

Vernier Caliper Working Principle

The vernier caliper is a versatile and precise measuring instrument. It consists of two main parts: a fixed main scale and a sliding vernier scale. The main scale provides primary measurements, typically in millimeters or inches, while the vernier scale offers additional precision by dividing each main scale increment further.
When measuring with a vernier caliper, one of its jaws remains stationary, while the other moves to accommodate the object. The improvement in precision is akin to a fine-tuning mechanism, allowing readings to a fraction of the smallest unit on the main scale through vernier subtleties.
Here's how it works:

• The main scale gives a base reading, contributing to whole-number measurements.
• The vernier scale refines this with its minute divisions, offering further precision.
• The objective is to align the vernier and main scales accurately, reducing the smallest measurable increment.
• When no object is placed, if the zeros align perfectly, the tool is error-free.

While using a vernier caliper seems straightforward, a small misalignment can cause a zero error, a common challenge in accurate measurements.

Measuring Instruments

Measuring instruments like vernier calipers, micrometers, and gauges are essential tools in science and engineering. Each offers varying degrees of precision depending on their design and intended use.
Vernier calipers bridge the gap between rough measuring tools like rulers and high-precision devices such as micrometers. They are often used in laboratories and workshops for tasks where a medium level of accuracy is required, such as measuring diameters, lengths, or depths.
Key features of measuring instruments:

• Precision and Accuracy: Devices like the vernier caliper offer increased accuracy by limiting errors through precise scale increments.
• Usability: Many measuring tools are designed for ease of use and rapid reading, making them efficient for repetitive tasks.
• Calibration: Proper setup is crucial, as incorrect calibration can lead to consistent errors across measurements.
• Durability: High-quality instruments resist wear and tear, maintaining accuracy over extended periods.

Understanding each instrument's function and limitations ensures optimal performance and trustworthy data collection.

Least Count Calculation

The least count of a measuring instrument defines its measuring capability, representing the smallest value it can accurately signify. For a vernier caliper, the least count is crucial because it determines the level of detail achieved in measurement.
The least count is determined by the formula:
\[\text{Least Count} = \text{Smallest Division on Main Scale} - \text{Smallest Division on Vernier Scale}\]
For instance, if the main scale has a smallest division of 1 mm and the vernier scale subdivides one of these divisions into 10 parts, then the least count calculation is:
\[\text{Least Count} = 1 \, \text{mm} / 10 = 0.1 \, \text{mm}\]
This ability to measure to 0.1 mm means every vernier caliper reading can tell you where precisely between the millimeter divisions your measurement lands, increasing the certainty of your data.
The least count also helps in identifying zero error. If an initial reading occurs without an object, any discrepancy observed due to non-zero alignment of scales results in a calculation using the least count to correct this error, ensuring exact results in subsequent measurements.