A spherical solid ball of volume V is made of a material of density ρ_1 . It is falling through a liquid of density ρ_2 ( ρ_2 < ρ_1 ). Assume that the - Physics MCQ AIEEE 2026 | ExamTest.live

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A spherical solid ball of volume V is made of a material of density ρ_{1} . It is falling through a liquid of density ρ_{2} (ρ_{2} < ρ_{1}). Assume that the liquid applies a viscous force F_{viscous} = - k v^{2} . The terminal speed of the ball is:

Solution & Step-by-step Explanation

At terminal velocity v_{T}, the net force on the ball is zero.Forces acting: Weight (W = ρ_{1} V g), Buoyancy (F_{B} = ρ_{2} V g), and Viscous force (F_{v} = k v_{T}^{2}). W - F_{B} - F_{v} = 0 ρ_{1} V g - ρ_{2} V g = k v_{T}^{2} V g (ρ_{1} - ρ_{2}) = k v_{T}^{2} ⟹ v_{T} = \frac{V g ( ρ _{1} - ρ _{2} )}{k}

Try it yourself before checking the explanation above.

A spherical solid ball of volume V is made of a material of density ρ_{1} . It is falling through a liquid of density ρ_{2} (ρ_{2} < ρ_{1}). Assume that the liquid applies a viscous force F_{viscous} = - k v^{2} . The terminal speed of the ball is:

\frac{V g ( ρ _{1} - ρ _{2} )}{k}

\frac{V g ρ _{1}}{k}

\frac{V g ρ _{1}}{k}

\frac{V g ( ρ _{1} - ρ _{2} )}{k}

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