A hollow sphere of volume V is floating on water surface with half...

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 ?

Options

A $\frac{V}{2}$
B $\frac{V}{3}$
C $\frac{V}{4}$
D $V$

Correct answer

A. $\frac{V}{2}$

Step-by-step solution

When a body (sphere) is half immersed, then Upthrust = weight of sphere

\frac{V}{2} \times \rho_{\text{liq }} \times g=\nu \times \rho \times g \therefore \quad \rho=\frac{\rho_{\text{liq }}}{2}

When body (sphere) is fully immersed then, Upthrust = weight of sphere + weight of water pourd in sphere

V \times \rho_{\text{liq }} \times g=V \times \rho \times g+V^{\prime} \times \rho_{\text{liq }} \times g V \times \rho_{\text{liq }}=\frac{v \times \rho_{\text{liq }}}{2}+V^{\prime} \times \rho_{\text{liq }} V^{\prime}=\frac{V}{2}

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