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 = [tex] \frac{4}{3}\pi R^{3} [/tex] , 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= [tex] 1000*\frac{4}{3}*\frac{22}{7}*(0.2)^{3}*9.8 [/tex]
= 328.5 N
Now, mass of the sphere = density of Styrofoam×Volume of sphere
= [tex] 300*\frac{4}{3}\pi (0.2)^{3} [/tex]
=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
