A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ₀. After sometime, the ball falls with constant velocity. The viscous force on the ball is :
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Question

A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ₀. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

G1 Physics · Accepted Answer

At terminal velocity: Acceleration = 0 Therefore: mg - F(B) - F(v) = 0 So: F(v) = mg - F(B) Volume of ball: V = m/ρ Buoyant force: F(B) = ρ₀Vg = ρ₀(m/ρ)g Hence: F(v) = mg[1 - ρ₀/ρ] According to the source paper, this corresponds to Option D.