Question

$V_{e} = \sqrt{\frac{2GM}{R}} = \sqrt{\frac{2G \times \rho \times \frac{4\pi R^{3}}{3}}{R}} \Rightarrow V_{e} \propto \sqrt{\rho} \times R$

$${\frac{\left( V_{e} \right)_{B}}{\left( V_{e} \right)_{A}} = \sqrt{\frac{\rho_{B}}{\rho_{A}}} \times \frac{R_{B}}{R_{A}} = \sqrt{\frac{0.1\rho_{A}}{\rho_{A}}} \times \left( \frac{0.1R_{A}}{R_{A}} \right) }{\frac{\left( V_{e} \right)_{B}}{\left( V_{e} \right)_{A}} = \frac{1}{10} \times \frac{1}{\sqrt{10}} }{\left( V_{e} \right)_{B} = \frac{10 \times 1000}{10\sqrt{10}} = 100\sqrt{10}\text{ }m/sec}$$