The velocity of a small ball of mass $M$ and density $d$, when dropped in a container filled with glycerine be

Question

The velocity of a small ball of mass $M$ and density $d$, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $\frac{d}{2}$, then the viscous force acting on the ball will be

Accepted Answer

When the velocity is constant, the net force is zero. The forces acting are gravity ($Mg$ downwards), buoyant force ($F_B$ upwards), and viscous force ($F_v$ upwards). So, $Mg = F_B + F_v$. The buoyant force $F_B = V \rho_{liquid} g = V (d/2) g$. Since $M = Vd$, $V = M/d$. Thus $F_B = (M/d) * (d/2) * g = Mg/2$. Therefore, $F_v = Mg - F_B = Mg - Mg/2 = Mg/2$.

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