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
B
V3
C
V4
D
V

Solution

## The correct option is A $$\dfrac{V}{2}$$Given the body is half immersed in the water. Let $$\rho$$ be the density of water and $$m$$ be the mass of the sphere initially.$$\Rightarrow mg=\dfrac{V}{2}\rho g$$Let $$V_0$$ volume is added to the sphere. Then the weight of sphere $$=mg+V_0\rho g$$After it is completely immersed:Buoyancy force $$=V\rho g$$Both the forces should be equal:$$\Rightarrow mg+V_o\rho g=V\rho g$$$$\Rightarrow V_0=\dfrac{V}{2}$$Physics

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