Question

If the ratio of the linear densities (denier) of two circular fibers is 3, the corresponding ratio of their diameters, (rounded off to two decimal places), is \(\underline{\hspace{2cm}}\).

Hint:

For fibers, the ratio of linear densities is proportional to the square of the ratio of their diameters.

Answer 1

Correct Answer: 1.7

The linear density of a fiber is proportional to the square of its diameter. Therefore, if the ratio of the linear densities is 3, the ratio of the diameters \( D_1 \) and \( D_2 \) is given by: \[ \frac{D_1}{D_2} = \sqrt{3} \approx 1.732. \] Thus, the ratio of the diameters is \( 1.73 \).