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
Diffcult
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(a)When body (sphere) is half immersed, then
upthrust = weight of sphere
==> $\frac{V}{2} \times {\rho _{{\rm{liq}}}} \times g = V \times \rho \times g$
upthrust = weight of sphere
==> $\frac{V}{2} \times {\rho _{{\rm{liq}}}} \times g = V \times \rho \times g$
$\rho = \frac{{{\rho _{{\rm{liq}}}}}}{2}$
When body (sphere) is fully immersed then,
Upthrust = wt. of sphere + wt. of water poured in sphere
==> $V \times {\rho _{{\rm{liq}}}} \times g = V \times \rho \times g + V' \times {\rho _{{\rm{liq}}}} \times g$
==> $V \times {\rho _{{\rm{liq}}}} = \frac{{V \times {\rho _{{\rm{liq}}}}}}{2} + V' \times {\rho _{{\rm{liq}}}}$==> $V' = \frac{V}{2}$
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