GravitationHard

Question

Two spherical planets P and Q have the same uniform density ρ, masses MP and MQ and surface areas A and 4A respectively. A spherical planet R also has uniform density ρ and its mass is (MP + MQ). The escape velocities from the planets P, Q and R are VP, VQ and VR, respectively. Then

Options

A.VQ > VR > VP
B.VR > VQ > VP
C.VR / VP = 3
D.VP / VQ =

Solution


By calculation, if Mass of P = m
and Radius of P = R
Then Mass of Q = 8M
and radius of Q = 2R
and Mass of R = 9M
and radius of R = 91/3R



∴ VR > VQ = VP

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