First slide

Pressure in a fluid-mechanical properties of fluids

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

V/2
B

V/3
C

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 = wt. of sphere + wt. of water poured in sphere
$\begin{array}{l} \Rightarrow V \times ρ_{liq} \times g = V \times ρ \times g + V^{'} \times ρ_{liq} \times g \\ \Rightarrow V \times ρ_{iiq} = \frac{V \times ρ_{liq}}{2} + V^{'} \times ρ_{liq} \Rightarrow V^{'} = \frac{V}{2} \end{array}$

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