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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