Two spherical planets P and Q have the same uniform density , masses M_ P and M_ Q and surface areas A and 4A respectively. A spherical planet R also has uniform density and its mass is (M_ P +M_ Q ) . The escape velocities from the planets

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Two spherical planets P and Q have the same uniform density , masses M_ P and M_ Q and surface areas A and 4A respectively. A spherical planet R also has uniform density 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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Correct answer: B. V_ R >V_ Q >V_ P

Here Planets P and Q have the same uniform density ' ' and surface areas A and 4 A respectively. Let the mass of P, M_ P be m . Then m= 4 3 r³= 4 3 [ A 4 ]^ 3 / 2 The mass of M_ Q = 4 3 [ 4 A 4 ]^ 3 / 2 =8 ~m The mass of Planet R=8 ~m + m =9 ~m If the radius of P=r Then the radius of Q=2 r [ r_ Q = ( 4 A 4 )^ 3 / 2 =2 ( A 4 )^ 3 / 2 ] and radius of R=9^ 1 / 3 r [ array l M_ R =M_ P +M_ Q r_ R ³=r³+(2 r)³=9 r³ array ] As we know, escape velocity from the planet aligned V_ e = 2 G M R & v_ P = 2 G M_ P R_ p = 2 G m r

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