Question

A less-dense liquid of density rho1 floats on top of a more-dense liquid of density rho2. A uniform cylinder of length l and density rho, with rho1

Answer 1

Answer:

Explanation:

Given

$\rho=density\ of\ cylinder\\\rho_1=less\ dense\ cylinder\\\rho_2=more\ dense\ cylinder$

Suppose V is the volume of a cylinder

Also $L_1=length\ in\ less\ dense\ part\\L_2=length\ in\ dense\ part\\L=length\ of\ cylinder\\V=A\times L\\where\ A=area\ of\ cross-section$

Now, we can write

The weight of the cylinder is supported by the buoyant forces of two liquids

$\rho Vg=\rho_1 V_1g+\rho_2 V_2g\\\rho ALg=\rho_1 A\times L_1g+\rho_2 A\times L_2g\\\\\rho L=\rho_1 L_1+\rho_2 L_2\\Also, L=L_1+L_2$

using the above equation we can write

$L_2=\frac{\rho-\rho_1}{\rho_2-\rho_1}\cdot L\\\frac{L_2}{L}=\frac{\rho-\rho_1}{\rho_2-\rho_1}$