Answer
Choice (b) 0.25%
Work Step by Step
The frequency $f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$.
We need to find $\frac{\Delta f}{f} = \frac{f-f_0}{f_0}$.
If we call $k$ the new force constant, then . . .
$\frac{\Delta f}{f} = \frac{(1/2\pi)\sqrt{k/m} - (1/2\pi)\sqrt{k_0/m}}{(1/2\pi)\sqrt{k_0/m}}$
Cancelling all the pre-factors and common terms, we get . . .
$\frac{\Delta f}{f} = \frac{\sqrt{k} - \sqrt{k_0}}{\sqrt{k_0}} = \frac{\sqrt{k}}{\sqrt{k_0}} - 1 = \frac{\sqrt{1005}}{\sqrt{1000}} - 1 = 2.5 \times 10^{-3} = 0.25\%$. This is choice (b).
