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

Question

The velocity of a small ball of mass $M$ and density $d$, when dropped into a container filled with a viscous fluid, becomes constant after some time. If the density of the fluid is $d/3$, then the viscous force acting on the ball in this steady state will be

Professor PC Thomas Classes · Answer

(c) : When the ball reaches a constant (terminal) velocity, the net force acting on it is zero. Thus, the upward forces (Buoyant force $F_B$ + Viscous force $F_v$) equal the downward force (Weight $W = Mg$). So, $F_v = W - F_B$. The volume of the ball is $V = M/d$. The buoyant force is $F_B = V 	imes 	ext{density of fluid} 	imes g = (M/d) 	imes (d/3) 	imes g = Mg/3$. Therefore, the viscous force is $F_v = Mg - Mg/3 = 2Mg/3$.