A ball of mass m and radius r is released in viscous liquid....

A ball of mass $m$ and radius $r$ is released in viscous liquid. The value of its terminal velocity is proportional to
(A) $(1 / r)$ only
(B) $\mathrm{m} / \mathrm{r}$
(C) $(m / r)^{1 / 2}$
(D) $m$ only

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Terminal Velocity

Terminal velocity is the constant speed that an object attains when the force of gravity is balanced by the resistive forces (such as drag) acting on it. In a viscous medium, an object reaches terminal velocity when the acceleration ceases, meaning that the net force acting on the object becomes zero.

Stokes’ Law

Stokes’ Law describes the drag force experienced by a sphere moving through a viscous fluid at low Reynolds numbers. It states that the drag force is proportional to the radius of the sphere and its velocity, typically expressed as F_drag = 6??rv, where ? is the viscosity of the fluid.

Force Equilibrium

At terminal velocity, the gravitational force (possibly reduced by the buoyant force) balances the drag force. This equilibrium condition is crucial in deriving relationships between physical quantities such as mass and radius with terminal velocity.

Proportional Reasoning in Fluid Dynamics

Proportional reasoning involves deducing how one variable scales with another given a physical law. In this context, by equating the gravitational force (or effective weight) to a drag force that depends on the sphere’s radius and velocity, one can determine the proportional dependency of terminal velocity on the mass and radius of the sphere.

Transcript

Please give Ace some feedback