A sphere completely submerged in water is tethered to the bottom with a string. The tension in the string is one-third the weight of the sphere. What is the density of the sphere

Explanation:

Assume the sphere has a volume of 1 m³ and the water is fresh.

It displaces 1 m³ of water with mass of 1000 kg

If m is the mass of the sphere, then balancing forces on the sphere gives us

downward forces of

mg + mg/3

and upward buoyancy force of 1000g N which is the weight of the water displaced.

(4/3)mg = 1000g

 (4/3)m = 1000

        m = 750 kg

ρ = 750 kg/m³