Two spherical planets P and Q have the same uniform density ρ , masses M P and M Q , with 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
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(b, d)
Sol. V es = 
= 
= 
R
V es ∝ R
Sarface area of P = A = 4 π R P 2
Surface area of Q = 4A = 4 π R Q 2
⇒ R Q = 2R p
mass R is M R = M P + M Q
= 
+ 
⇒ R R 3 = R P 3 + R Q 3
= 9R P 3
R R = 9 1/3 R P ⇒ R R > R Q > R P
Therefore V R > V Q > V P
= 9 1/3 and 
= 
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