How Is the Mass of a Hollow Sphere Calculated in Water?

[dnp33]

Homework Statement

A hollow plastic sphere is held below the surface of a fresh water lake by a cord anchored to the bottom of the lake. The sphere has a volume of 0.65 m^3 and the tension in the cord is 842 N. What is the mass of the sphere, in kg? Enter your answer using 3 decimal places, don't enter the units

Homework Equations

$$\rho *V*g=F$$
F=mg

The Attempt at a Solution

because the system is in equilibrium
F tension + Force of gravity = Buoyant Force.
842N + (9.81m/s^2)m = (1000kg/m^3)(0.65m^3)(9.81m/s^2)
the answer turns out to be 564kg, unless I'm doing something really stupid.
but that seems to be really high for a hollow plastic sphere.

 

[Delphi51]

Your calc looks correct! And your physical intuition. I guess whoever made up the question estimated the mass rather high.

 

[dnp33]

yeah i can't think of anything that I'm doing wrong, it just seems really weird that the mass would be so high.
when i worked out the density of the ball it was lower than that of water so it should float it just seems weird thinking about something that heavy floating.

 

[nvn]

dnp33: Your answer is correct. Let's say the hollow sphere in your given problem is made of polyvinyl chloride (PVC) plastic, has a wall thickness of t = 148.12 mm, and contains air at atmospheric pressure. The density of polyvinyl chloride is rho_p = 1400 kg/m^3. Can you compute the mass of this sphere? Neglect the density of air.