A beaker is filled with water. A ball of mass m and density $\rho$

Question

A beaker is filled with water. A ball of mass m and density $\rho$ < $\rho$_water is tied to a string. The other end of the string is then tied to the bottom of the beaker so that the ball is completely submerged. What is the tension in the string? C) mg

Quizplus · Accepted Answer

The tension in the string is equal to the weight of the ball minus the buoyant force. Since the ball is completely submerged, the buoyant force is equal to the weight of the water displaced by the ball. Because the ball is denser than water, it displaces a volume of water less than its own volume, so the buoyant force is less than the weight of the ball. Therefore, the tension in the string is greater than the weight of the ball. Choice A is the only option that is greater than mg.

A Beaker Is Filled with Water ρ\rhoρ ρ\rhoρ water Is Tied to a String

A Beaker Is Filled with Water $\rho$ $\rho$ _water Is Tied to a String