Question

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

• A. $\{1+(n-1\left)p\right\}p$
• B. $\{1+(n+1\left)p\right\}p$
• C. $\{2+(n+1\left)p\right\}p$
• D. $\{2-(n+1\left)p\right\}p$

Answer 1

The correct option is A $\{1+(n-1\left)p\right\}p$

$\begin{array}{c}d=densityofcylinder\\ A=areaofcross-sectionalofcylinder\\ U\sin glawoffloation,\\ weightofcylinder=upthrustbytwoliquids\\ L\times A\times d\times g\\ =n\rho \times \left(pL\times A\right)g+\rho \left(L-pL\right)Ag\\ d=np\rho +\rho \left(1-p\right)=\left(np+1-p\right)\rho \\ d=\left\{1+\left(n-1\right)p\right\}\rho \end{array}$

Hence,

option $\left(A\right)$ is correct answer.