First slide

Pressure in a fluid-mechanical properties of fluids

Question

A ball of density $ρ_{0}$ falls from rest from a point p onto the surface of a liquid of density $ρ$ in time T. It enters the liquid, stops, moves up, and returns to P in a total time 3T. Neglect viscosity, surface tension and splashing. The ratio of $\frac{ρ}{ρ_{0}}$ is ________

Moderate

Solution

It strikes the surface of liquid with velocity v₁ = gT in water (liquid) its time of flight.
$T = \frac{2 v_{1}}{(\frac{ρ}{ρ_{0}} - 1) g} = \frac{2 g T}{(\frac{ρ}{ρ_{0}} - 1) g} \Rightarrow \frac{ρ}{ρ_{0}} = 3$

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