What is the maximum mass that can hang without sinking from a 40- cm diameter styrofoam sphere in water? assume the volume of the mass is negligible compared to that of the sphere?

Adding this information to the question, density of Styrofoam is 300 kg/m³.

Let us first calculate the buoyant force on the Styrofoam sphere. It is equal to the weight of water displaced by the sphere when fully immersed.

∴ Fb= ρVg

Here, ρ is density of water = 1000 kg/m³

V is the volume of the sphere = , R is the radius of the sphere equal to 20 cm.

g is the acceleration due to gravity =9.8 m/s²

Substituting the values we get,

Fb=

= 328.5 N

Now, mass of the sphere = density of Styrofoam×Volume of sphere

=

=10.05 kg

Gravitational force on the sphere = mg

Fg= 10.05×9.8 =98.5 N

Net force on the sphere= Buoyant force ₋ Gravitational force

=328.5 ₋ 98.56 = 230 N

This is the maximum weight that can be hung from the Styrofoam without sinking in water.

To get maximum mass, m= Maximum weight/ Acceleration due to gravity

= 230÷9.8 = 23.4 g