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A cylinder of radius R and height H is floating upright in
water and a portion remains above the waterline. The density
of water is ρ. The cylinder is made of two different materials;
its upper half has density ρA ; its lower half has density ρB .
Derive an expression for the difference between the pressure at
the cylinder’s lower (submerged) surface and atmospheric
pressure, in terms of system parameters.

Respuesta :

Answer:

Pressure difference between Top and Bottom of the cylinder is given as

[tex]\Delta P = \frac{gH}{2}(\rho_A + \rho_B)[/tex]

Explanation:

As we know that the force due to pressure is balanced by the weight of the cylinder

So we will have

[tex]F = mg[/tex]

so we have

[tex]\Delta P \pi R^2 = mg[/tex]

so we have

[tex]\Delta P \pi R^2 = \pi R^2(\rho_A(\frac{H}{2}) + \rho_B(\frac{H}{2}))g[/tex]

so we have

[tex]\Delta P = \frac{gH}{2}(\rho_A + \rho_B)[/tex]

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