\(\mathrm{m}_{1} \mathrm{R}_{1}=\mathrm{m}_{2} \mathrm{R}_{2}\)

Remaining mass \(\times(2-\mathrm{R})=\) cavity mass \(\times(\mathrm{R}-1)\)

\(\left(\frac{4}{3} \pi \mathrm{R}^{3} \rho-\frac{4}{3} \pi l^{3} \rho\right)(2-\mathrm{R})=\frac{4}{3} \pi l^{3} \rho \times(\mathrm{R}-1)\)

\(\left(\mathrm{R}^{3}-1\right)(2-\mathrm{R})=\mathrm{R}-1\)

\(\left(\mathrm{R}^{2}+\mathrm{R}+1\right)(2-\mathrm{R})=1\)