A 4.7 kg solid sphere,made of metal whose density is 4000 kg/m3,is suspended by a cord.The density of water is 1000 kg/m³.When the sphere is immersed in water,the tension in the cord is closest to: A)35 N B)40 N C)46 N D)52 N E)58 N

Question

Quizplus · Accepted Answer

We can start by using Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object.

The buoyant force (FB) on the sphere is:
FB = density of water x volume of sphere submerged x acceleration of gravity 
FB = 1000 kg/m³ x (4/3 π (0.1m)³) x 9.81 m/s² 
FB = 33.09 N

We can also find the weight of the sphere (W):
W = mass x acceleration of gravity 
W = 4.7 kg x 9.81 m/s² 
W = 46.17 N

Since the sphere is suspended by a cord, the tension in the cord (T) must be equal to the weight of the sphere minus the buoyant force:
T = W - FB 
T = 46.17 N - 33.09 N 
T = 13.08 N

Therefore, none of the given answer choices are correct. However, we can assume that the answer choices are rounded and estimate that the closest answer is A) 35 N.

A 47 Kg Solid Sphere,made of Metal Whose Density Is 4000