Q. 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) $V$
Explanation
(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
$\Rightarrow V \times \rho_{liq} \times g = V \times \rho \times g + V' \times \rho_{liq} \times g$
$\Rightarrow V \times \rho_{liq} = \frac{V \times \rho_{liq}}{2} + V^{'} \times \rho_{liq} \Rightarrow V^{'} = \frac{V}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.