Answer: a) B = 6811N
b) m = 603.2kg
c) 86.8%
Explanation: Buoyant force is a force a fluid exerts on a submerged object.
It can be calculated as:
[tex]B=\rho_{fluid}.V_{obj}.g[/tex]
where:
[tex]\rho_{fluid}[/tex] is density of the fluid the object is in;
[tex]V_{obj}[/tex] is volume of the object;
g is acceleration due to gravity, is constant and equals 9.8m/s²
a) For the hollow plastic sphere, density of water is 1000kg/m³:
[tex]B=10^{3}.0.695.9.8[/tex]
B = 6811N
b) Anchored to the bottom, the forces acting on the sphere are Buoyant, Tension and Force due to gravity:
B = T + [tex]F_{g}[/tex]
B = T + mg
mg = B - T
[tex]m=\frac{B - T}{g}[/tex]
Calculating:
[tex]m=\frac{6811 - 900}{9.8}[/tex]
m = 603.2kg
c) When the shpere comes to rest on the surface of the water, there are only buoyant and gravity acting on it:
B = m.g
[tex]\rho_{w}.V_{sub}.g=m.g[/tex]
[tex]V_{sub}=\frac{m}{\rho_{w}}[/tex]
[tex]V_{sub}=\frac{603.2}{1000}[/tex]
[tex]V_{sub}[/tex] = 0.6032m³
Fraction of the submerged volume is:
[tex]\frac{V_{sub}}{V_{obj}}[/tex] = [tex]\frac{0.6932}{0.695}[/tex] = 0.868
