Question

A spherical solid ball of volume V is made of a material of density ρ₁. It is falling through a liquid of density ρ₂(ρ₂ <ρ₁). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous = −kv² (k>0). The terminal speed of the ball is

$square root of fraction numerator Vg left parenthesis straight rho subscript 1 minus straight rho subscript 2 right parenthesis over denominator straight k end fraction end root$
$Vgρ subscript 1 over straight k$
$square root of Vgρ subscript 1 over straight k end root$
$fraction numerator Vg left parenthesis straight rho subscript 1 minus straight rho subscript 2 right parenthesis over denominator straight k end fraction$

Solution

square root of fraction numerator Vg left parenthesis straight rho subscript 1 minus straight rho subscript 2 right parenthesis over denominator straight k end fraction end root

ρ₁Vg − ρ₂Vg = kv₂^T
$rightwards double arrow space straight V subscript straight T space equals space square root of fraction numerator Vg space left parenthesis straight rho subscript 1 minus straight rho subscript 2 right parenthesis over denominator straight k end fraction end root$

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Mechanical Properties Of Fluids

Some More Questions From Mechanical Properties of Fluids Chapter

A jar filled with two non-mixing liquids 1 and 2 having densities ρ₁ and ρ₂ respectively. A solid ball, made of a material of density ρ₃, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
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Mechanical Properties Of Fluids

Some More Questions From Mechanical Properties of Fluids Chapter

A jar filled with two non-mixing liquids 1 and 2 having densities ρ1 and ρ2 respectively. A solid ball, made of a material of density ρ3, is dropped in the jar. It comes to equilibrium in the position shown in the figure.Which of the following is true for ρ1, ρ2 and ρ3?

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