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(A) Let $\rho$ be the density of the material of the sphere and $\rho_w$ be the density of water.When the sphere is floating half-immersed,the weight

Vedclass · Accepted Answer

$V/2$

Vedclass · Answer

(A) Let $\rho$ be the density of the material of the sphere and $\rho_w$ be the density of water.When the sphere is floating half-immersed,the weight of the sphere is balanced by the buoyant force:$W_{sphere} = F_{buoyant}$$V \cdot \rho \cdot g = (V/2) \cdot \rho_w \cdot g$$\rho = \rho_w / 2$Now,let $V'$ be the volume of water poured inside the sphere so that it just sinks. For the sphere to sink,the total weight (sphere + water) must equal the buoyant force when the sphere is fully submerged:$W_{total} = F_{buoyant, total}$$(V \cdot \rho \cdot g) + (V' \cdot \rho_w \cdot g) = V \cdot \rho_w \cdot g$Substitute $\rho = \rho_w / 2$:$V \cdot (\rho_w / 2) \cdot g + V' \cdot \rho_w \cdot g = V \cdot \rho_w \cdot g$Divide by $\rho_w \cdot g$:$V/2 + V' = V$$V' = V - V/2 = V/2$Therefore,the minimum volume of water to be poured is $V/2$.

$A$ hollow sphere of volume $V$ is floating on the 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?

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