question_answer

Two solids P and Q float in water. It is observed that P floats with half of its volume immersed and Q floats with \[\frac{{{2}^{rd}}}{3}\] of its volume is immersed. The ratio of densities of P and Q is

A)  \[\frac{4}{3}\]     

B)  \[\frac{3}{4}\]

C)  \[\frac{2}{3}\]    

D)  \[\frac{3}{2}\]

Correct Answer: B

Solution :

:  For solid P, Let \[{{V}_{p}}\] and \[\rho p\] be volume and density of solid P respectively                                  As the solid P is floating in water,              \[\therefore \] Weight of P = weight of water displaced By P \[{{V}_{p}}{{\rho }_{p}}g=\frac{{{V}_{p}}}{2}{{\rho }_{water}}g\] \[{{\rho }_{p}}=\frac{1}{2}{{\rho }_{water}}\]                            ??.(i) Similarly, for solid Q \[{{V}_{Q}}{{\rho }_{Q}}g=\frac{2}{3}{{V}_{Q}}{{\rho }_{water}}g\]   \[{{\rho }_{Q}}=\frac{2}{3}{{\rho }_{water}}\]                         ????..(ii) Divide (i) by (ii), we get \[\frac{{{\rho }_{p}}}{{{\rho }_{Q}}}=\frac{3}{4}\]