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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

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Answer:

Step-by-step 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

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