A) \[\frac{V}{2}\]
B) \[\frac{V}{3}\]
C) \[\frac{V}{4}\]
D) \[V\]
Correct Answer: A
Solution :
In floating condition Upthrust = weight of sphere \[\frac{V}{2}\times {{\rho }_{liq}}\times g=V\times \rho \times g\] \[\Rightarrow \] \[\rho =\frac{{{\rho }_{liq}}}{2}\] When ball fully immersed, then Upthrust = wt. of sphere + wt. of water poured into the sphere \[V\times {{\rho }_{liq}}\times g=V\times \rho \times g+V\times {{\rho }_{liq}}\times g\] \[V\times {{\rho }_{liq}}=\frac{V\times {{\rho }_{liq}}}{2}+V\times {{\rho }_{liq}}\] \[V=\frac{v}{2}\]
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