A solid wooden sphere of volume 0.0100 m³ floats freely exactly one-half submerged in a liquid of density 800 kg/m³. A lightweight cord is now tied to the sphere and is used to pull the sphere under the surface and hold it completely submerged. What is the tension in the cord?

Question

Quizplus · Accepted Answer

When the sphere is floating, the buoyant force is equal to its weight. Since it is one-half submerged, the volume of water displaced is equal to half the volume of the sphere. Using the density of water, the weight of the displaced water can be calculated and set equal to the weight of the sphere. This gives the weight of the sphere as 0.0196 N.

When the sphere is completely submerged, it experiences an upward buoyant force of the weight of the displaced water (now equal to the volume of the sphere). The weight of the sphere is still 0.0196 N, so the tension in the cord must be equal to the weight of the sphere plus the buoyant force, or 0.0196 N + (0.0100 m^3 * 800 kg/m^3 * 9.81 m/s^2) = 39.2 N. Therefore, the answer is C.

A Solid Wooden Sphere of Volume 0