Question

A body floats with one third of its volume outside water and three fourth of its volume, outside another liquid. The density of another liquid is:

• A. $ \frac{9}{4}gm/cm^{3} $
• B. $ 4.9\,gm/cm^{3} $
• C. $ \frac{8}{3}gm/cm^{3} $
• D. $ \frac{3}{8}gm/cm^{3} $

Answer 1

Answer: (C)

Let $V$ be the volume of the body.
Weight of body is equal to weight of water displaced
$=2 / 3 \vee \times 1 \times g$
In another liquid, weight of body
$=1 / 4 \vee \times \rho \times g$
$\therefore 2 / 3 \vee g=1 / 4 \vee \rho g$
or $\rho=8 / 3\, gm / cm ^{3}$