Question

Two non-mixing liquids of densities $\rho$ and $n\rho (n>1)$ are put in a container. The height of each liquid in $h$. 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. $\left[2+(n+1)p\right]\rho$
• C. $\left[2+(n-1)p\right]\rho$
• D. $\left[1+(n-1)p\right]\rho$

Answer 1

The correct option is D $\left[1+(n-1)p\right]\rho$

$\rho$ and $n\rho \to$ Density

$(n>1)$

$now:$

weight and buoyant system

$dvg=\frac{\rho v}{L}(L-\rho L)g+\frac{n\cdot \rho v}{L}\left(\rho L\right)g$

$d=\rho +(n-1){\rho }^2$

$d=[1+(n-1\left)\rho \right]\rho$

Correct option is (D).