Properties Of Solids And Liquids Question 274
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
Options:
A)$ V/2 $
B)$ V/3 $
C)$ V/4 $
D)V
Show Answer
Answer:
Correct Answer: A
Solution:
When body (sphere) is half immersed, then upthrust = weight of sphere
therefore $ \frac{V}{2}\times {\rho _{ρliq}}\times g=V\times \rho \times g $ \ $ \rho =\frac{{\rho _{ρliq}}}{2} $
When body (sphere) is fully immersed then, Upthrust = wt. of sphere + wt. of water poured in sphere
therefore $ V\times {\rho _{ρliq}}\times g=V\times \rho \times g+V’\times {\rho _{ρliq}}\times g $
therefore $ V\times {\rho _{ρliq}}=\frac{V\times {\rho _{ρliq}}}{2}+V’\times {\rho _{ρliq}} $
therefore $ V’=\frac{V}{2} $
