2021 Mechanical Properties of FluidsViscosity and Terminal Velocity Medium Question 2 of 2 in Viscosity and Terminal Velocity

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:

A $Mg$
B $\frac{3}{2}Mg$
C $2\,Mg$
D $\frac{Mg}{2}$

The answer is D.

Solution

Density of ball = d, density of glycerine = $\frac{d}{2}$; volume V, so Mg = Vdg Buoyant force $F_B = V\frac{d}{2}g = \frac{Mg}{2}$ At constant velocity, $F_{net} = 0$: $F_B + F_v = Mg$ $F_v = Mg - \frac{Mg}{2} = \frac{Mg}{2}$

Concept viscous force at terminal velocity

Viscosity and Terminal Velocity in past papers

2 questions from this chapter have appeared across 2 exam years.