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Question

A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water?

A
V2
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B
V3
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C
V4
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D
V
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Solution

The correct option is A V2
Given the body is half immersed in the water. Let ρ be the density of water and m be the mass of the sphere initially.
mg=V2ρg
Let V0 volume is added to the sphere. Then the weight of sphere =mg+V0ρg
After it is completely immersed:
Buoyancy force =Vρg
Both the forces should be equal:
mg+Voρg=Vρg
V0=V2

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