Question

A cube of ice floats partly in water and partly in oil. Find the ratio of the volume of ice immersed in water to that in oil. Specific gravity of oil is $0.8$ and that of ice is $0.9$

Answer 1

Specific gravity of water ${\rho }_w=1gm/cc$

Specific gravity of ice ${\rho }_{ice}=0.9gm/cc$

Specific gravity of kerosene ${\rho }_k=0.8gm/cc$

Now,

$V_{ice}=V_k+V_w$

here,

$V_k=$ Volume of ice in the kerosene

$V_w=$ Volume of ice in the water

$V_{ice}=$ Volume of ice

Thus,

$V_{ice}\times {\rho }_{ice}\times g=V_k\times {\rho }_k\times g+V_w\times \rho w\times g$

$(V_k+V_w)\times {\rho }_{ice}=V_k\times {\rho }_k+V_w\times \rho w$

$(V_k+V_w)\times 0.9=V_k\times 0.8+V_w\times 1$

$\left(0.1\right)V_w=\left(0.1\right)V_k$

$\frac{V_w}{V_k}=1$

$V_w:V_k=1:1$