A spherical solid ball of volume V is made up of material of density ρ . It is falling through a liquid of density σ ( σ

Question

A spherical solid ball of volume V is made up of material of density ρ . It is falling through a liquid of density σ ( σ < ρ ) . Assume that the liquid applies a viscous force on the ball that is proportional to square of the terminal speed v T ​ , F = − K v T 2 ​ , ∀ ( K > 0 ) , then the terminal speed of the ball is ( g = acceleration due to gravity)

TestHub · Accepted Answer

The condition for terminal speed v T ​ is given by, weight ( W ) = buoyant force ( f ) + viscous force ( F ) We know, W = ρ V g , f = σV g and F = K v T 2 ​ ∴ ρ V g = σV g + K v T 2 ​ v T ​ = K ( ρ − σ ) V g ​ ​

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