The mass m of a vibrating string can be determined using the following relationship - Scottish Highers Physics - Question 25 - 2023

To find the mass $m$, rearrange the formula:

$f = \sqrt{\frac{T}{4ml}}$

Squaring both sides gives:

$f^2 = \frac{T}{4ml}$

Rearranging for $m$:

$m = \frac{T}{4lf^2}$

Substituting in the values:

• $T = 92 \text{ N}$
• $l = 0.63 \text{ m}$
• $f = 110 \text{ Hz}$

Calculating:

$m = \frac{92}{4 \times 0.63 \times (110)^2}$

Evaluating: $m = \frac{92}{4 \times 0.63 \times 12100}$

Calculating the denominator: $4 \times 0.63 \times 12100 \approx 30422.4$

So, $m \approx \frac{92}{30422.4} \approx 0.00302 \text{ kg}$

This can be written as: $m \approx 3.0 \times 10^{-3} \text{ kg}$

Thus, the correct answer is A: $3.0 \times 10^{-3} \text{ kg}$.