Question

Two solids A and B float in water. It is observed that A floats with half of its volume immersed and B floats with 2/3 of its volume immersed. Compare the densities of A and B

• A. 4 : 3
• B. 2 : 3
• C. 3 : 4
• D. 1 : 3

Answer 1

The correct option is (C) 3 : 4

$Asweknow,$

$f_b=Mg;\text{buoyant}forcewillbeequaltotheweightoftheliquiddisplaced.$

$f_{b_1}={\left(Mg\right)}_1⟶\left(1\right)$

$f_{b_2}={\left(Mg\right)}_2⟶\left(2\right)$

$\frac{\left(1\right)}{\left(2\right)}=\frac{V_A{\sigma }_{A}g}{V_B{\sigma }_{B}g}=\frac{V_{As}\delta g}{V_{Bs}\delta g}$

$where{\sigma }_a=densityofA$

${\sigma }_b=densityofB$

$\delta =densityoffluid$

$\frac{{\sigma }_A}{{\sigma }_B}=\frac{\frac{1}{2}}{\frac{2}{3}}$

$\frac{{\sigma }_A}{{\sigma }_B}=\frac{3}{4}$

Therefore the correct answer is option (C)