Question

What is the least count of commonly available vernier? (A) \(0.01 \mathrm{~cm}\) (B) \(0.001 \mathrm{~cm}\) (C) \(0.0001 \mathrm{~cm}\) (D) \(0.1 \mathrm{~cm}\)

Short answer

The least count of a commonly available vernier is (A) \(0.01 \,cm\).

Step-by-step solution

Recognize the information given

In this problem, we are given four choices for the least count of a commonly available vernier. We need to find the correct one by knowing the actual least count of the vernier scale.

Calculate the least count of the vernier scale

To find the least count, we need to know the difference between the main scale and the vernier scale. The least count of the vernier scale can be calculated using the formula: \(Least \, Count = \frac{1 \, MSD}{10}\) where MSD is the least count of the main scale, which is usually 1 mm or 0.1 cm.

Compare the calculated least count with the given choices

Using the formula from Step 2, we can calculate the least count: \(Least \, Count = \frac{1 \, MSD}{10} = \frac{0.1 \, cm}{10} = 0.01 \, cm\)

Choose the correct answer

By comparing the calculated least count with the given choices, we can see that the correct answer is: (A) \(0.01 \,cm\).

Key concepts

Vernier Scale

The vernier scale is an additional scale used in measurement devices like calipers and micrometers to provide precise readings. It operates on the principle that small increments can be measured by determining how many times a small unit fits into a larger unit. This allows for reading finer measurements than the main scale alone.

• The vernier scale works by aligning with the main scale as the measuring instrument is used.
• It typically consists of a sliding scale that moves alongside the main scale.
• Each division on the vernier scale slightly differs from the main scale, allowing for enhanced precision.
• This design reduces the possibility of parallax error, improving overall accuracy.

The ability to accurately measure small differences makes the vernier scale invaluable in scientific and engineering applications.

Main Scale Division

The main scale division (MSD) measures straightforward, baseline units on devices like vernier calipers. It represents the fundamental graduations upon which the vernier scale is based.

• Main scale divisions are typically larger and more widely spaced, making them easier to read at a glance.
• On a vernier caliper, the main scale usually measures in centimeters or millimeters, depending on the standard used.
• The smallest reading possible directly from the main scale is the main scale division's value.
• Precision measurements rely on how these main scale divisions are subdivided by the vernier scale.

Understanding the main scale division is crucial when calculating the device's least count, which determines measurement resolution.

Least Count Calculation

To achieve higher precision in measuring instruments, least count calculation is a fundamental concept. The least count indicates the smallest measurement that can be accurately read by the instrument.

• The formula for calculating the least count is: \( \text{Least Count} = \frac{\text{Value of 1 MSD}}{\text{Number of Divisions on the Vernier Scale}} \).
• For example, if the value of one main scale division (MSD) is 0.1 cm, and the vernier scale has 10 divisions, the least count is \( 0.01 \, \text{cm} \).
• This calculation helps in determining the instrument's precision, guiding users to read measurements more accurately.
• By understanding and using the least count, one can resolve smaller differences that would be missed by the main scale alone.

Grasping the least count concept helps improve the interpretation and accuracy of measurements in practical scenarios.

Measurement Accuracy

Measurement accuracy is critical in precision instruments like vernier calipers. It determines how close a measured value is to the actual value.

• Accuracy depends on both the calibration of the device and the user's skill in reading measurements.
• The least count plays a vital role in assessing measurement accuracy. A smaller least count generally means a higher potential for precise readings.
• Errors can result from misalignment, improper calibration, or human error when interpreting the scales.
• Utilizing a vernier caliper properly involves ensuring that the jaws are properly aligned and the device is zeroed before taking measurements.

For best results, regular calibration and proper handling of measuring instruments can significantly enhance measurement accuracy.