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

Answer 1

The correct option is A $\frac{V}{2}$

Given the body is half immersed in the water. Let $\rho$ be the density of water and $m$ be the mass of the sphere initially.

$\Rightarrow mg=\frac{V}{2}\rho g$

Let $V_0$ volume is added to the sphere. Then the weight of sphere $=mg+V_0\rho g$

After it is completely immersed:

Buoyancy force $=V\rho g$

Both the forces should be equal:

$\Rightarrow mg+V_o\rho g=V\rho g$

$\Rightarrow V_0=\frac{V}{2}$