Two spherical planets and have the same uniform density , masses and , and surface areas and , respectively. A spherical planet also has uniform density and its mass is . The escape velocities from the planets and , are and , respectively. Then
(A)
(B)
(C)
(D)
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The escape velocity on a spherical planet is given by r 2 G M . Because Q 's surface area is 4 times that of P , it must have twice the radius. Then, the volume is increased by a factor of 2 3 = 8 . This implies that M Q = 8 M P , because the densities of the planets are the same. The escape velocity of Q is thus 2 r P 2 G × 8 M P = 2 r P 2 G M P = 2 V P which satisfies condition ( D ) . Note that only one of the answers choices contains D, so this must be the answer.