# Escape velocities

Classical Mechanics Level 3

Two spherical planets $$P$$ and $$Q$$ have the same uniform density $$\rho$$, masses $$M_\rho$$ and $$M_{Q}$$, and surface areas $$A$$ and $$4A$$, respectively. A spherical planet $$R$$ also has uniform density $$\rho$$ and its mass is $$( M_P + M_Q)$$. The escape velocities from the planets $$P, Q$$ and $$R$$, are $$V_P, V_Q$$ and $$V_R$$, respectively. Then

(A) $$V_Q > V_R > V_P$$

(B) $$V_R > V_Q > V_P$$

(C) $$V_R/V_P = 3$$

(D) $$V_P/V_Q = \frac{1}{2}$$

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