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The length of a bar is 25.4 cm measured by a scale. Vernier coincidence is 13.

* Determine the vernier constant in inch unit.

Answer :

To determine the vernier constant in inch unit, we first need to understand the concept of a vernier caliper and how it measures dimensions.

A vernier caliper is a precision instrument used to measure lengths. It consists of a main scale and a sliding vernier scale which helps in obtaining more precise measurements.

Step-by-Step Calculation

  1. Understanding Vernier Constant:

    • The vernier constant is the smallest measurement that can be taken with a vernier caliper and is also known as the Least Count. It's calculated as the difference between one main scale division and one vernier scale division.

  2. Usually, the Vernier Constant Formula is:
    [tex]\text{Vernier Constant} = \text{Smallest division on the main scale} - \text{Smallest division on the vernier scale}[/tex]

  3. Converting cm to inches:

    • Since the problem requires the vernier constant in inches, we must convert the measurement units. Usually, 1 inch equals 2.54 cm.

  4. Assume Typical Vernier Caliper Values:

    • A common setup is where one main scale division equals 1 mm (0.1 cm), and the vernier scale division might typically be slightly less. Assume the same below.

  5. Calculate in cm first (common step and simplistic estimation):

    • Suppose the smallest division on the main scale is 0.1 cm.
    • The smallest division on the vernier might be 0.09 cm.
    • Vernier Constant = 0.1 cm - 0.09 cm = 0.01 cm.

  6. Convert Vernier Constant to inches:

    • Using 1 inch = 2.54 cm, convert 0.01 cm to inches:
      [tex]\text{Vernier Constant} = \frac{0.01 \text{ cm}}{2.54} \approx 0.00394 \text{ inches}[/tex]

Therefore, in typical conditions and calculations, the vernier constant would be approximately 0.00394 inches.

Conclusion

Using the typical values for the smallest divisions on the main and vernier scales and converting from cm to inches, we have determined the vernier constant in inch unit as approximately 0.00394 inches.

This step-by-step approach provides a clear understanding of how to determine the vernier constant and its conversion to inches.

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