What is the maximum mass that can hang without sinking from a 20-cm diameter styrofoam sphere in water? assume the volume of the mass is negligible compared to that of the sphere.

the maximum mass that can hang without sinking is 2.93 kg

Explanation:

Given: details:

sphere diameter  d = 20 cm

so, radius r = 10 cm  = 0.10 m

density of the Styrofoam sphere D = 300 kg/m3

sphere volume  

                                                   =4.18*10^{-3} m^3

we know that

mass  M = Density * Volume

                                  = (300)(4.18*10^{-3} m3)

                                  =1.25 kg

mass of the water displace = volume *density  of water

                                                 = 4.18*10^{-3} m3 * 1000

                                                 = 4.18 kg

The difference between the mass of water and mass of styrofoam is the amount of mass that the sphere can support

=4.18 kg  -1.25 kg

= 2.93 kg

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach