3.
A ball is falling through a viscous fluid at its terminal velocity. The magnitudes of the
forces acting on the ball are: gravitational force FG, drag force FD and buoyant force FB.
Which of the following conditions is true?
a. FG + FB + FD = 0
b. FG + FB = FD
c. FG – FB = FD
d. FG + FB = 2FD

Terminal Velocity Forces on Ball in Viscous Fluid: Correct Answer Revealed

A ball falling at terminal velocity through a viscous fluid experiences zero net force, where gravitational force downward balances upward drag and buoyant forces. The correct condition is c. FG – FB = FD.​

Forces Explained

Gravitational force (FG = mg) pulls the ball downward. Buoyant force (FB = ρ_fluid V g) pushes upward per Archimedes’ principle, reducing effective weight. Drag force (FD = 6πηrv via Stokes’ law) opposes motion and increases with velocity until balance at terminal velocity.​​

Net force equation: FG downward = FD upward + FB upward, so FG = FD + FB or FG – FB = FD.​

Option Analysis

• a. FG + FB + FD = 0: Incorrect; forces have directions—cannot all sum to zero without signs.

• b. FG + FB = FD: Wrong; buoyant force aids drag against gravity, not adds to it.

• c. FG – FB = FD: Correct; effective gravitational force (weight minus buoyancy) equals drag.​

• d. FG + FB = 2FD: Incorrect; no basis for doubling drag or adding buoyancy to gravity.

The phenomenon of a ball falling through viscous fluid at terminal velocity captivates physics students, balancing gravitational force FG, drag force FD, and buoyant force FB. At terminal velocity, constant speed means net force is zero: downward FG equals upward FD + FB, or FG – FB = FD. This principle applies in Stokes’ law scenarios for spheres in liquids like oil or glycerin.​

Physics of Terminal Velocity

When dropped, the ball accelerates until drag (proportional to velocity) and buoyancy match effective gravity. Equation: mg−ρVg=6πηrvtmg−ρVg=6πηrvt, simplifying to FG – FB = FD. Real-world demos with steel balls in silicone fluid confirm this balance occurs rapidly.​​

Common Exam Misconceptions

Many confuse buoyancy direction—FB always upward, reducing net downward force. Option b wrongly adds FB to FG; option a ignores vector nature. Practice with varied densities sharpens understanding for competitive exams.​

Keywords: viscous fluid terminal velocity, forces on falling ball, FG FB FD balance, Stokes law drag, buoyant force physics