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9-1.Fluid Mechanics
medium
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
A
$\frac{{{d_0}}}{d}$
B
$\frac{{d{d_0}}}{{d + {d_0}}}$
C
$\frac{{d - {d_0}}}{d}$
D
$\frac{{d{d_0}}}{{d - {d_0}}}$
Solution
(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]$
==> $\frac{{{V_{out}}}}{{{V_0}}} = \frac{{d – {d_0}}}{d}.$
Standard 11
Physics