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

• A. $V / 2$
• B. $V / 3$
• C. $V / 4$
• D. $V$

Answer 1

Answer: (A)

When body (sphere) is half immersed,
then Upthrust $=$ Weight of sphere
$\Rightarrow \frac{V}{2} \times \rho_{ liq } \times g=V \times \rho \times g$
$\therefore \rho=\frac{\rho_{ liq }}{2}$
When body (sphere) is fully immersed then,
Upthrust = Wt. of sphere + Wt. of water poured in sphere
$\Rightarrow V \times \rho_{ liq } \times g=V \times \rho \times g+V^{\prime} \times \rho_{ liq } \times g$
$\Rightarrow V \times \rho_{ liq }=\frac{V \times \rho_{ liq }}{2}+V^{\prime} \times \rho_{ liq }$
$\Rightarrow V^{\prime}=\frac{V}{2}$