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.
• C. $V / 4$
• D. V

Answer 1

Answer: (A)

$V / 2$

Answer 2

When body (sphere) is half immersed, then

upthrust = weight of sphere

⇒ ∴

When body (sphere) is fully immersed then,

Upthrust = wt. of sphere + wt. of water poured in sphere

⇒ $V \times \rho _ { \text {liq } } \times g = V \times \rho \times g + V ^ { \prime } \times \rho _ { \text {liq } } \times g$

⇒ $V ^ { \prime } = \frac { V } { 2 }$