First slide

Fluid statics

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?

Moderate

A

$\frac{V}{2}$
B

$\frac{V}{3}$
C

$\frac{V}{4}$
D

V

Solution

When body (sphere) is half immersed, then Upthrust = weight of sphere
$\Rightarrow \frac{V}{2} \times ρ_{liq} \times g = V \times ρ \times g ∴ ρ = \frac{ρ_{liq}}{2}$
When body (sphere) is fully immersed then,
Upthrust = weight of sphere + weight of water poured in sphere
$\Rightarrow V \times ρ_{liq} \times g = V \times ρ \times g + V' \times ρ_{liq} \times g$
$\Rightarrow V \times ρ_{liq} = \frac{V \times ρ_{liq}}{2} + V^{'} \times ρ_{liq} \Rightarrow V^{'} = \frac{V}{2}$

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