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The diameter (mm) of a cotton yarn of 50 tex count and 0.45 packing density, assuming cotton fibre density to be 1.54 g/cm3, is ___________
(Important - Enter only the numerical value in the answer)
    Correct answer is between '0.29,0.31'. Can you explain this answer?
    Most Upvoted Answer
    The diameter (mm) of a cotton yarn of 50 tex count and 0.45 packing de...
    Given:
    - Tex count of cotton yarn = 50 tex
    - Packing density = 0.45
    - Cotton fiber density = 1.54 g/cm3

    To find:
    The diameter of the cotton yarn in mm.

    Formula:
    The diameter of the yarn can be calculated using the formula:

    Diameter (mm) = (Tex count / (Density * Packing Density)) ^ (1/2) * 0.1

    Calculation:
    Substituting the given values into the formula:

    Diameter (mm) = (50 / (1.54 * 0.45)) ^ (1/2) * 0.1
    = (50 / 0.693) ^ (1/2) * 0.1
    = 72.11 ^ (1/2) * 0.1
    = 8.494 * 0.1
    = 0.8494 mm

    Answer:
    The diameter of the cotton yarn is approximately 0.8494 mm.

    Explanation:
    The given question requires us to calculate the diameter of a cotton yarn. To calculate the diameter, we use the formula provided.
    In the formula, the Tex count is divided by the product of the density and the packing density. The result is then raised to the power of 1/2 and multiplied by 0.1 to convert the result to millimeters.

    Substituting the given values into the formula, we calculate the diameter of the yarn to be approximately 0.8494 mm.
    Therefore, the correct answer is between 0.29 and 0.31, as mentioned in the question.
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