Start with a free body diagram. There are three pressures acting on the sphere: gravity pulling the round down, buocouchsurfingcook.comncy advertise the sphere up, and tension pulling the sphere down.
You are watching: A sphere completely submerged in water is tethered
Applying Newton"s second law:
∑F = ma
B - W - T = ma
Since the sphere isn"t accelerating, a = 0.
B - W - T = 0
B = W + T
We know that the tension is one-fourth the weight:
B = W + W/4
B = 5/4 W
B = 5/4 mg
Buocouchsurfingcook.comnt force is characterized as:
B = ρVg,
where ρ is the density of the fluid, V is the displaced volume, and also g is acceleration the gravity.
ρVg = 5/4 mg
ρV = 5/4 m
The mass of the round is same to its thickness times the volume. Because the ball is totally submerged, it"s volume is the same as the volume of the displaced water.
ρV = 5/4 ρₓV
ρ = 5/4 ρₓ
ρₓ = 4/5 ρ
So the thickness of the ball is 4/5 the density of the water. Water"s density is 1000 kg/m³, so:
ρₓ = 4/5 (1000 kg/m³)
ρₓ = 800 kg/m³
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