Answer:
Explanation:
Given
[tex]\rho=density\ of\ cylinder\\\rho_1=less\ dense\ cylinder\\\rho_2=more\ dense\ cylinder[/tex]
Suppose V is the volume of a cylinder
Also [tex]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\\[/tex]
Now, we can write
The weight of the cylinder is supported by the buoyant forces of two liquids
[tex]\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[/tex]
using the above equation we can write
[tex]L_2=\frac{\rho-\rho_1}{\rho_2-\rho_1}\cdot L\\\frac{L_2}{L}=\frac{\rho-\rho_1}{\rho_2-\rho_1}[/tex]
