A vertical solid cylinder is floating on a liquid with a density of ? in a cylin

Question

A vertical solid cylinder is floating on a liquid with a density of ? in a cylindrical tank as shown in the figure (1a). The axis of the solid cylinder and tank coincides. The diameters of the solid cylinder and tank are d and D respectively. The solid cylinder is than pushed down gradually with a force of F until it comes to rest at a lower level as shown in the figure (1b). Determine: a) The rise, h, of the water level in the tank as observed from outside and b) The amount of sinking distance, s, of the solid cylinder as observed from outside.

Explanation / Answer

density of liquid = p gravitational force = g Applying Archimedes principle, the applied force f should be equal to change in mass of water displaced This means, F = p*pi*d^2*(h+s)*g.........(1) Also the net volume of water risen should be equal to volume of cylinder immersed after F is applied. This means, pi*d^2*s= pi*(D^2-d^2)*h........(2) Solving (1) and (2), we get, h= F/p*g*D^2 s= (F/p*g)*(1/d^2-1/D^2)

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