Question

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?

Answer 1

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 =
`(4)/(3)\pi R^(3)` , 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=
`1000*(4)/(3)*(22)/(7)*(0.2)^(3)*9.8`

= 328.5 N

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

=
`300*(4)/(3)\pi (0.2)^(3)`

=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