= Solution
The <sagitta> is the maximum distance between the circular track and its chord. The perpendicular bisector of a chord of length $L$ gives a right triangle with hypotenuse $R$ and sides $L/2$ and $R-s$. Hence
$$
s=R-\sqrt{R^2-L^2/4}=\frac{L^2}{8R}+O(L^4/R^3)
\simeq\boxed{\frac{|q|BL^2}{8p}}.
$$
At fixed <electric charge>, <magnetic field> and lever arm, $p=|q|BL^2/(8s)$, so differentiation and <propagation of uncertainty> give
$$
\boxed{\frac{\sigma(p)}p=\frac{\sigma(s)}s=\frac{8p\,\sigma(s)}{|q|BL^2}.}
$$
Thus a fixed spatial <measurement uncertainty> produces a relative <momentum> uncertainty growing linearly with $p$. If <momentum> is expressed in $\mathrm{GeV}/c$, $B$ in tesla, $L,s$ in metres and $z=q/e$, restore the usual conversion $p=0.2998|z|BR$.
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