10 main scale divisions = 1cm, 10 vernier divisions = 9 main scale divisions, zero of Vernier scale is to the right of the zero marking of the main scale with 6th Vernier division... 10 main scale divisions = 1cm, 10 vernier divisions = 9 main scale divisions, zero of Vernier scale is to the right of the zero marking of the main scale with 6th Vernier division coinciding with a main scale division and the actual reading for length measurement is 4.3 cm with 2nd Vernier divisions coinciding with a main scale graduation. Estimate the length.
Understand the Problem
The question is asking us to determine the estimated length based on the given measurements involving a main scale and a vernier scale. It provides specific details about the divisions on both scales and the position of the vernier scale's zero point, as well as the actual reading of the length measurement. We will approach this by calculating the lengths based on the given information and combining them to find the total estimated length.
Answer
Total Length = Main Scale Reading + Vernier Scale Reading.
Answer for screen readers
The estimated total length is given by the equation: $$ \text{Total Length} = \text{Main Scale Reading} + \text{Vernier Scale Reading} $$
Steps to Solve
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Identify the Main Scale Reading Start by observing the main scale and reading the value up to the last visible line before the vernier scale starts. This is typically measured in centimeters or millimeters.
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Determine the Vernier Scale Reading Next, look at the vernier scale. Find the line on the vernier scale that aligns exactly with a line on the main scale. This reading represents the additional length to be added to the main scale reading.
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Calculate the Value of Each Division Calculate the value of one division on the vernier scale. For example, if the main scale divisions are in millimeters and the vernier scale has more divisions in the same length, use the following formula: $$ \text{Vernier Scale Value} = \frac{\text{Length of Main Scale}}{\text{Number of Vernier Scale Divisions}} $$
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Combine the Readings Add the main scale reading and the vernier scale reading to find the total estimated length: $$ \text{Total Length} = \text{Main Scale Reading} + \text{Vernier Scale Reading} $$
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Express the Final Measurement Finally, express the total length with the appropriate units, combining all the previous calculations.
The estimated total length is given by the equation: $$ \text{Total Length} = \text{Main Scale Reading} + \text{Vernier Scale Reading} $$
More Information
This estimation technique is commonly used in precision measurements, where a main scale and a vernier scale provide more accurate readings than either scale alone. The vernier scale allows for much finer measurements, making it a valuable tool in various scientific and engineering applications.
Tips
- Misreading the Scales: Ensure that you read both scales accurately, noting the correct divisions.
- Ignoring Units: Always confirm that you are using consistent units (e.g., mm or cm) throughout your calculation.
- Wrong Calculation of Vernier Value: Be careful when calculating the value per division using the correct formula.
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