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$V/2$
B$V/3$
C$V/4$
D$V$
Diffcult
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A$V/2$
a (a)When body (sphere) is half immersed, then
upthrust = weight of sphere
==> $\frac{V}{2} \times {\rho _{{\rm{liq}}}} \times g = V \times \rho \times g$
$\rho = \frac{{{\rho _{{\rm{liq}}}}}}{2}$
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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