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

Step-by-step 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* 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* L_1g+\rho_2 A* 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=(\rho-\rho_1)/(\rho_2-\rho_1)\cdot L\\(L_2)/(L)=(\rho-\rho_1)/(\rho_2-\rho_1)`