A 4.7-kg solid sphere, made of metal whose density is 4000 kg/m3, hangs by a light cord. When the sphere is immersed in water, what is the tension in the cord

T = 34.54 N

Explanation:

First we find the buoyant force acting on the sphere, due to displaced water. For that purpose, we need to find the volume of water displaced by the sphere.

Volume of Water Displaced = V = (Mass of Sphere) / (Density of metal)

V = 4.7 kg / (4000 kg/m³)

V = 0.001175 m³

Now, the buoyant force is given as:

F = (Density of Water) (V) (g)

F = (1000 kg/m³) (0.001175 m³) (9.8 m/s²)

F = 11.52 N

Now, we find the weight of the sphere:

W = mg = (4.7 kg) (9.8 m/s²)

W = 46.06 N

Since, both the tension force (T) and buoyant force act in upward direction, while the weight of sphere act in downward direction. Therefore,

W = T + F

T = W - F

T = 46.06 N - 11.52 N

T = 34.54 N