A ball of density ρ0 falls from rest at t = 0 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 at t = 3T0. Neglect viscosity, surface tension and splashing. The ratio \frac{\rho}{\left(\rho\right)

Engineering

Physics

Statics

Question

A ball of density ρ₀ falls from rest at t = 0 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 at t = 3T₀. Neglect viscosity, surface tension and splashing. The ratio $\frac{ρ}{ρ_{0}}$ is equal to

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For downward moment of the ball inside the liquid
v = v + at

$0 = gt - \frac{F_{b} - Mg}{M} \times \frac{T}{2}$

$(\frac{F_{b}}{M} - g) \frac{T}{2} = gF$

$\frac{F_{b}}{M} = 3 g$

$(\frac{M}{ρ_{0}}) \frac{ρg}{M} = 3 g$

$\frac{ρ}{ρ_{0}} = 3$ .

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