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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 $$\dfrac{V}{2}$$
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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