Question

You are provided with a hollow iron ball $A$ of volume $15c{m}^3$ mass $12g$ and a solid iron ball $B$ of mass $12g$. Both are placed on the surface of water contained in a large tub. Which ball with sink? Give reason for your answer.

Answer 1

Mass of ball $A=12g$
Mass of ball $B=12g$
Density of iron $=8gc{m}^3$
Volume of the hollow iron ball $A=15c{m}^3$
Volume of the hollow iron ball $B=$ Mass/ density $=12/8=1.5c{m}^{-3}$
hollow in ball $B$ will sink
Upthrust on ball $B$ is $1.5gf$which is less weight $12gf$, while upthrust on ball $A$ will be $15gf$ if it is fully submerged, which is greater than weight $12gf$, so if will float with its submerged part for which the upthrust becomes equal to its weight which is $12gf$.