A) 4 : 3
B) 2 : 3
C) 3 : 4
D) 1 : 2
Correct Answer: B
Solution :
Upthrust = weight of body For A, \[\frac{{{V}_{A}}}{2}\times {{\rho }_{W}}\times g={{V}_{A}}\times {{\rho }_{A}}\times g\Rightarrow {{\rho }_{A}}=\frac{{{\rho }_{W}}}{2}\] For B, \[\frac{3}{4}{{V}_{B}}\times {{\rho }_{W}}\times g={{V}_{B}}\times {{\rho }_{B}}\times g\Rightarrow {{\rho }_{B}}=\frac{3}{4}{{\rho }_{W}}\] (Since 1/4 of volume of B is above the water surface) \ \[\frac{{{\rho }_{A}}}{{{\rho }_{B}}}=\frac{{{\rho }_{W}}/2}{3/4\ {{\rho }_{W}}}=\frac{2}{3}\]
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