= Solution
Let $M$ be the mass of a complete uniform sphere of radius $a$. The intact marble has $I_1=2Ma^2/5$. Each removed bubble has mass $M/8$, radius $a/2$, and centre a distance $a/2$ from the rolling axis. By the <parallel axis theorem>, each removes
$$
\frac25\frac M8\left(\frac a2\right)^2+\frac M8\left(\frac a2\right)^2
=\frac{7}{160}Ma^2.
$$
Thus $M_2=3M/4$, $I_2=2Ma^2/5-7Ma^2/80=5Ma^2/16$, and $I_2/(M_2a^2)=5/12$. The two accelerations are therefore $(5/7)g\sin\alpha$ and $(12/17)g\sin\alpha$. From rest, distance is proportional to acceleration, so
$$
\boxed{\frac{s_1(t)}{s_2(t)}=\frac{85}{84}.}
$$
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