Question

Consider two identical small glass balls dropped into two identical containers, one filled with water and the other with oil. Which ball will reach the bottom of the container first? Why?

Short answer

Answer: The ball dropped into the container filled with water will reach the bottom first. This is because the increased drag force in oil, due to its higher viscosity, slows down the ball's motion to a greater extent compared to the effects of slightly stronger buoyancy in water.

Step-by-step solution

Identify the forces acting on the balls

As the balls are dropped into their respective containers, there are three primary forces acting on them: gravitational force, buoyancy, and the drag force due to the fluids. Gravitational force pulls the balls downward, buoyancy opposes this downward motion, and the drag force acts in the direction opposite to the balls' movement.

Compare the effect of buoyancy in water and oil

Buoyancy is the upward force that results from the pressure difference caused by an object submerged in a fluid. Buoyancy depends on the volume and the density of the fluid displaced by the object. Since the two balls are identical and have the same volume, they will displace the same amount of fluid. The density of water is higher than that of oil, so the buoyancy force in water will be greater than that in oil. However, since the difference in density is not too significant, we can conclude that the buoyancy forces will not have a major impact on the balls' motion in both fluids.

Compare the drag forces in water and oil

The drag force acts opposite to the direction of motion and is proportional to the velocity of the object squared. The drag force mainly depends on the viscosity of the fluid. The viscosity of oil is greater than that of water, which means that the drag force acting on the ball falling through oil will be higher than that on the ball falling through water. Consequently, the resistance to the ball's motion will be greater in oil compared to water.

Combine the effects of buoyancy and drag forces

When analyzing the combined effects of buoyancy and drag on the balls, we can conclude the following: The buoyancy force will be slightly stronger in water than in oil, but the difference will not have a significant impact on the balls' motion. However, the drag force will be much greater in oil due to its higher viscosity, significantly slowing down the ball's motion through oil compared to water.

Determine the winner

Considering the combined effects of buoyancy and drag forces, we can conclude that the ball dropped into the container filled with water will reach the bottom first. The increased drag force in oil, due to its higher viscosity, slows down the ball's motion to a greater extent compared to the effects of slightly stronger buoyancy in water.