Question

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

Answer 1

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

Using Archimedes' principle, we get:

$LAdg=\left(pL\right)A\left(n\rho \right)g+(1-p)LA\rho g$

$\Rightarrow d=(1-p)\rho +\left(pn\right)\rho$

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