Question

An object of mass M and density ρ released from rest while under water. The object feels a viscous drag from the water with a drag constant K. What is the terminal speed of the ball?

free body and what laws

What do you expect to happen to the terminal velocity as the density of the ball approaches the density of the water?

A. As the density of the object approaches the density of the water, the terminal speed increases radically, approaching infinity.

B. As the density of the object approaches the density of the water, the terminal speed is unaffected since the density of the water only appears in the terminal speed equation through the calculation of the drag constant.

C. As the density of the object approaches the density of the water, the speed decreases radically, approaching zero.

D. Whether the density of the object approaching the density of water increases or decreases the terminal speed of the object in water depends on the total mass of the object.

Answer 1

when a object falls under fluid it experies two forces first bouyant force due to displced water and viscous force due to friction between layers of fluid acts upward and second is weight of object which acts downward so when this two forces becomes equal then object aquire a terminal speed

which remain constant after that

so.

Viscous force and bouyont force

where rhof is density of water and A is surface area of object

and weight of object is

so when these both become equal means

so, terminal velocity is

so when

then terminal speed of object approches zero

so option C)