To determine the percentage error in the measurement of $ C $, which is related to $ p $, $ q $, $ r $, and $ s $ as:

$ C = \frac{p q^2}{r^3 \sqrt{s}} $

we first express it in terms of powers:

$ C = p^1 q^2 r^{-3} s^{-1/2} $

The percentage error in $ C $ can be calculated using the formula for the propagation of error, which is:

$ \left(\frac{\Delta C}{C}\right)_{\max} = \left|\frac{\Delta p}{p}\right| + 2\left|\frac{\Delta q}{q}\right| + 3\left|\frac{\Delta r}{r}\right| + \frac{1}{2}\left|\frac{\Delta s}{s}\right| $

Given the percentage errors for $ p $, $ q $, $ r $, and $ s $ are $ 1\% $, $ 2\% $, $ 3\% $, and $ 2\% $ respectively, we substitute these values into the formula:

$ \left(\frac{\Delta C}{C}\right)_{\max} = 1\% + 2 \times 2\% + 3 \times 3\% + \frac{1}{2} \times 2\% $

Calculating each part:

Contribution from $ p $: $ 1\% $

Contribution from $ q $: $ 4\% $ (since $ 2 \times 2\% = 4\% $)

Contribution from $ r $: $ 9\% $ (since $ 3 \times 3\% = 9\% $)

Contribution from $ s $: $ 1\% $ (since $ \frac{1}{2} \times 2\% = 1\% $)

Adding these contributions together:

$ 1\% + 4\% + 9\% + 1\% = 15\% $

Thus, the maximum percentage error in the measurement of $ C $ is $ 15\% $.