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Question

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


Solution

Mass of ball $$A=12g$$
Mass of ball $$B=12g$$
Density of iron $$=8 gcm^3$$
Volume of the hollow iron ball $$A=15 cm^3$$
Volume of the hollow iron ball $$B=$$ Mass/ density $$=12/8=1.5\ cm^{-3}$$
hollow in ball $$B$$ will sink
Upthrust on ball $$B$$ is $$1.5 gf$$which is less weight $$12gf$$, while upthrust on ball $$A$$ will be $$15 gf$$ 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 $$12gf$$.

Physics

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