A) \[V/2\]
B) \[V/3\]
C) \[V/4\]
D) V
Correct Answer: A
Solution :
When body (sphere) is half immersed, then upthrust = weight of sphere Þ \[\frac{V}{2}\times {{\rho }_{\text{liq}}}\times g=V\times \rho \times g\] \ \[\rho =\frac{{{\rho }_{\text{liq}}}}{2}\] When body (sphere) is fully immersed then, Upthrust = wt. of sphere + wt. of water poured in sphere Þ \[V\times {{\rho }_{\text{liq}}}\times g=V\times \rho \times g+V'\times {{\rho }_{\text{liq}}}\times g\] Þ \[V\times {{\rho }_{\text{liq}}}=\frac{V\times {{\rho }_{\text{liq}}}}{2}+V'\times {{\rho }_{\text{liq}}}\]Þ \[V'=\frac{V}{2}\]
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