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Two spherical planets P and Q have the same uniform density $ρ$ , masses M_P and M_Q and surface areas A and 4A respectively. A spherical planet R also has uniform density $ρ$ 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

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V_Q >V_R >V_P

V_R >V_Q >V_P

V_R /V_P =3

V_P / V_Q = 1 /2

answer is B.

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Detailed Solution

$\begin{array}{l} V_{P} = \sqrt{\frac{2 GM}{R}}, V_{Q} = \sqrt{\frac{2 G 8 M}{2 R}} = 2 V_{P} \\ V_{R} = \sqrt{\frac{2 G 9 M}{9^{1 / 3} R}} = 9^{1 / 3} V_{P} \end{array}$

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