question_answer

A jar is filled with two non-mixing liquids 1 and 2 having densities \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\], respectively. A solid ball, made of a material of density \[{{\rho }_{3}}\], is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for \[{{\rho }_{1}},{{\rho }_{2}}\] and\[{{\rho }_{3}}\]?                                                                                                                              [AIEEE 2008]

A)  \[{{\rho }_{1}}<{{\rho }_{2}}<{{\rho }_{3}}\]                       

B)  \[{{\rho }_{1}}<{{\rho }_{3}}<{{\rho }_{2}}\]

C)  \[{{\rho }_{3}}<{{\rho }_{1}}<{{\rho }_{2}}\]           

D)       \[{{\rho }_{1}}>{{\rho }_{3}}>{{\rho }_{2}}\]

Correct Answer: B

Solution :

[b] Heavier liquid settles down at the bottom

So,

, otherwise, ball will sink

, otherwise, ball will float in liquid 1