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? A)zero B)2.00 N C)39.2 N D)4.00 N E)78.4 N

Question

Quizplus · Accepted Answer

When the sphere is floating freely, the weight of the sphere is balanced by the buoyant force. Hence, we can write:

Weight of sphere = Buoyant force

ρgV = ρflgV/2

where ρ is the density of the sphere, g is acceleration due to gravity, V is volume of the sphere, and ρfl is the density of the liquid. Solving for V, we get V = 0.00125 m3.

When the sphere is completely submerged, the tension in the cord is equal to the weight of the sphere. The weight of the sphere is given by:

Weight of sphere = ρgV

= (5500 kg/m3)(9.81 m/s2)(0.00125 m3)

= 68.24 N

Therefore, the tension in the cord is 68.24 N, which is closest to option C (39.2 N). Hence, the correct answer is C.

A Solid Wooden Sphere of Volume 0