First slide

Fluid statics

Question

A body floats with one-third of its volume outside water and $\frac{3}{4}$ of its volume outside another liquid. The density of another liquid is:

Moderate

A

$\frac{9}{4} g / cc$
B

$\frac{4}{9} g / cc$
C

$\frac{8}{3} g / cc$
D

$\frac{3}{8} g / cc$

Solution

Suppose volume and density of the body be V and $ρ$ respectively The, according to law of floatation in water.
Weight = upthrust
in water $Vρg = \frac{2}{3} {Vρ}_{w} g - - - - - - - (1)$
In liquid, V $ρg = \frac{1}{4} {Vρ}_{L} g - - - - - (2)$
From (1) and (2), $\frac{2}{3} {Vρ}_{w} g = \frac{1}{4} {Vρ}_{L} g$
or $\frac{ρ_{L}}{ρ_{w}} = \frac{\frac{2}{3}}{\frac{1}{4}} = \frac{8}{3}$
or $ρ_{L} = \frac{8}{3} ρ_{w} = \frac{8}{3} \times 1 g / cc$

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