A hollow sphere of volume V is floating on water surface with half immersed in it. What should be mi

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9-1.Fluid Mechanics

hard

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

$V/2$

$V/3$

$V/4$

$V$

Solution

(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
==> $V \times {\rho _{{\rm{liq}}}} \times g = V \times \rho \times g + V' \times {\rho _{{\rm{liq}}}} \times g$
==> $V \times {\rho _{{\rm{liq}}}} = \frac{{V \times {\rho _{{\rm{liq}}}}}}{2} + V' \times {\rho _{{\rm{liq}}}}$==> $V' = \frac{V}{2}$

Standard 11

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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

Solution

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