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                                                                               [NEET - 2016]

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 :

[d]

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

\[\Rightarrow \]   \[d=(1-p)\rho +pn\,\rho =[1+(n-1)p]\rho \]