Question

A beach ball filled with air is pushed about 1 m below the surface of a swimming pool and released from rest. Which of the following statements are valid, assuming the size of the ball remains the same? (Choose all correct statements.) (a) As the ball rises in the pool, the buoyant force on it increases. (b) When the ball is released, the buoyant force exceeds the gravitational force, and the ball accelerates upward. (c) The buoyant force on the ball decreases as the ball approaches the surface of the pool. (d) The buoyant force on the ball equals its weight and remains constant as the ball rises. (e) The buoyant force on the ball while it is submerged is approximately equal to the weight of a volume of water that could fill the ball.

Short answer

Option (a), (b), (c) and (e) is the correct answer

Step-by-step solution

Step 1: Archimedes’ principle

When an object is partially or fully submerged in a fluid, the fluid exerts on the object an upward force called the buoyant force. According to Archimedes’ principle, the magnitude of the buoyant force is equal to the weight of the fluid displaced by the object:

$B={\rho }_{Fluid}g{V}_{disp}$

Where $V_{disp}$is the weight of fluid is displaced at $p$and${\rho }_{Fluid}$ is the density of the fluid.

Find which of the following statements are valid

• As per Archimedes’ principle, the buoyant force is increasing as the ball rises in the pool due to the force is equal to the fluid’s weight displaced by the object.
• The buoyant force is exceeding the gravitational force acting upward, when the ball is released.
• When the ball reaches the pool’s surface, the buoyant force is decreasing.
• And the buoyant force is equaltotheweightofthevolumeofwater, when the ball is submerged.

Hence option (a), (b), (c) and (e) is the correct answer for this question.