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
$\Rightarrow V\times {\rho }_{liq}\times g=V\times \rho \times g+V^{\prime }\times {\rho }_{liq}\times g$
$\Rightarrow V\times {\rho }_{liq}=\frac{V\times {\rho }_{liq}}{2}+V^{\prime }\times {\rho }_{liq}$
$\Rightarrow V^{\prime }=\frac{V}{2}$