A ball falling through a viscous liquid is acted upon by

Analyze the question: We need to list all the forces acting on a ball as it falls through a viscous liquid such as oil or glycerine.

Concept: When an object moves through a fluid, three forces can act on it:

1. Weight (W) acts downward. It is the pull of gravity, W = mg.
2. Upthrust (U) acts upward. The liquid pushes up on any object immersed in it. By Archimedes' principle, it equals the weight of the liquid displaced.
3. Viscous force (drag, F) acts upward, opposite to the direction of motion. It comes from the liquid's internal friction and increases with the ball's speed.

Solution:

• The ball is in a liquid, so it displaces liquid and experiences upthrust.
• Gravity acts on the ball, so its weight is present.
• The ball is moving through a viscous liquid, so there is a viscous drag opposing its motion.

So all three forces act on the ball:

W (down) = U + F (up) at terminal velocity

At first the weight is greater than U + F, so the ball accelerates. As its speed increases, the viscous force grows until the forces balance: W = U + F. The net force is then zero and the ball falls at constant terminal velocity.

Eliminating the options:

• A: Upthrust alone cannot be right, because the ball would not fall.
• B: This leaves out the viscous force, which is the key feature of a viscous liquid.
• C: This leaves out upthrust, which acts in any liquid.
• D: This includes all three forces, so it is correct.

Answer: D. Upthrust, the ball's weight and viscous force.

Exam tip: For any object falling through a fluid, remember the "W-U-V" check: Weight down, Upthrust and Viscous force up. At terminal velocity, W = U + V.