question_answer

Two non-mixing liquids of densities \[\rho \] and\[n\rho (n>1)\] are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length \[pL(p<1)\]in the denser liquid. The density d is equal to :-                                                          

A)  \[\{1+(n+1)p\}\rho \]   

B)  \[\{2+(n+1)p\}\rho \]

C)  \[\{2+(n-1)p\}\rho \]    

D)  \[\{1+(n-1)p\}\rho \]

Correct Answer: D

Solution :

                  \[LAdg=(pL)A(n\rho )g+(1-p)LA\rho g\] \[\Rightarrow \]\[d=(1-p)\rho +pn\,\rho =[1+(n-1)p]\rho \]