Question

An object is put, one by one, in three liquids having different densities. The object floats with $\frac{1}{9},\frac{2}{11}$ and $\frac{3}{7}$ parts of their volumes outside the surfaces in liquids of densities $d_1,d_2$ and $d_3$ respectively. Which of the following statement is correct?

• A. $d_1>d_2>d_3$
• B. $d_1>d_2<d_3$
• C. $d_1<d_2>d_3$
• D. $d_1<d_2<d_3$

Answer 1

The correct option is D $d_1<d_2<d_3$

For an object floating in water under equilibrium, the buoyant force acting upwards balances the weight of the object.

Hence $V_{imm}dg=mg$

Hence fraction of volume outside liquid=$1-\frac{V_{imm}}{V}$

$=1-\frac{m}{dV}$

Since $f_1<f_2<f_3$,

$d_1<d_2<d_3$