The fraction of a floating object of volume ${V_0}$ and density ${d_0}$ above the surface of a liquid of density $d$ will be
Medium
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(c)For the floatation ${V_0}{d_0}g = {V_{in}}\;d\;g$ ==> ${V_{in}} = {V_0}\frac{{{d_0}}}{d}$
${V_{out}} = {V_0} - {V_{in}} = {V_0} - {V_0}\frac{{{d_0}}}{d}$$ = {V_0}\left[ {\frac{{d - {d_0}}}{d}} \right]$
==> $\frac{{{V_{out}}}}{{{V_0}}} = \frac{{d - {d_0}}}{d}.$
${V_{out}} = {V_0} - {V_{in}} = {V_0} - {V_0}\frac{{{d_0}}}{d}$$ = {V_0}\left[ {\frac{{d - {d_0}}}{d}} \right]$
==> $\frac{{{V_{out}}}}{{{V_0}}} = \frac{{d - {d_0}}}{d}.$
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