A) \[\frac{9}{4}g/cc\]
B) \[\frac{4}{9}g/cc\]
C) \[\frac{8}{3}g/cc\]
D) \[\frac{3}{8}g/cc\]
Correct Answer: C
Solution :
Let V be volume of body and p its density then by law of floatation in water \[V\rho g=\frac{2}{3}V\times {{\rho }_{w}}g\] ?(i) [\[\because \]\[\frac{2}{3}V\] is immersed in water of density\[{{\rho }_{w}}\]] Similarly, in a liquid, \[V\rho g=\frac{1}{4}V\times {{\rho }_{l}}g\] ?(ii) From Eqs. (i) and (ii) \[\frac{2}{3}V{{\rho }_{w}}g=\frac{1}{4}V{{\rho }_{l}}g\] \[\Rightarrow \] \[\frac{{{\rho }_{l}}}{{{\rho }_{w}}}=\frac{8}{3}\] \[\Rightarrow \] \[\frac{{{\rho }_{t}}}{{{\rho }_{w}}}=\frac{8}{3}\] \[\therefore \] \[{{\rho }_{t}}=\frac{8}{3}{{\rho }_{w}}=\frac{8}{3}g\text{/}cc\] \[(\because {{\rho }_{w}}=1g\text{/}cc)\]
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