The masses of two spherical planets A and B are M_(A) and M_(B), surface areas are S and 9 S respectively. The mass of a spherical planet C is (M_(A) + M_(B)). If the densities of all the planets A, B, C are same, then the escape velocities V_(A), V_(B), V_(C) from the surface of these planets follow:

The masses of two spherical planets A and B are M_(A) and M_(B), surfa

1.	The masses of two spherical planets A and B are M_(A) and M_(B), surface areas are S and 9 S respectively. The mass of a spherical planet C is (M_(A) + M_(B)). If the densities of all the planets A, B, C are same, then the escape velocities V_(A), V_(B), V_(C) from the surface of these planets follow:
Answer» `V_(C)` GT `V_(B)` gt `V_(A)` `V_(B)` = 3`V_(A)` `V_(C)` lt `V_(B)` lt `V_(A)` `V_(C)` gt `V_(B)` lt `V_(A)` Solution :As area of B is 9 times area of A DENSITIES of all PLANETS is same, then `r_(B) = 3r_(A), M_(B) = 27 M_(A)` `r_(C ) = 3sqrt(28)r_(A) = 3.03 r_(A)` As `V_(A) = sqrt((2GM_(A))/(r_(A))) , V_(B) = sqrt((2GM_(B))/(r_(B))) , V_(A) = sqrt((2GM_(C ))/(r_(C )))` `rArr V_(A) = sqrt((2GM_(A))/(r_(A))), V_(B) = sqrt((2G xx 27 M_(A))/(3r_(A))) = sqrt((18 GM_(A))/(r_(A)))` `V_(C ) = sqrt((2GM_(C ))/(r_(C )))` `= sqrt((2G xx 28 xx M_(A))/(3.03 r_(A)))` `= sqrt((18.48 GM_(A))/(r_(A)))` `V_(C ) gt V_(B) gt V_(A)`