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uniform cylinder made of a material of density ‘ $ρ = 250 k g / m^{3}$ ’ is held at rest in a pool so that its upper circular surface is in level with the water surface. Length of the cylinder is $l = 20 c m$ and radius $r = 3.0 c m$ . When released, the cylinder jumps out of water moving vertically. Find velocity (in m/s) with which the cylinder leaves the water surface.
Density of water is $ρ_{0} = 1000 k g / m^{3}$ and acceleration due to gravity is $g = 10 m / s^{2}$ . Neglect all dissipative effects.

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answer is 2.

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Detailed Solution

$W_{u p t h r u s t} + W_{g r a v i t a t i o n a l f o r c e} = Δ K W_{u p t h r u s t} = \int_{0}^{1} ρ_{1} π r^{2} (1 - x) g d x W_{u p t h r u s t} = \frac{ρ_{1} π r^{2} g l^{2}}{2} W_{m g} = - m g l = - ρ_{s} π r^{2} l^{2} g$

Solving, $v = 2 m / s$ .

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