Question

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9) 

 

(1) 8 : 9 

(2) 5 : 4 

(3) 9 : 10 

(4) 1 : 1

Answer 1

Correct option is :  (4) 1 : 1 

\(\mathrm{v}_{1}=\) volume immersed in water.

\(\mathrm{v}_{2}=\)  volume immersed in oil.

\(v_{1}\ \rho_{w}\ g+v_{2}\ \rho_{\mathrm{o}} \ g=\left(v_{1}+v_{2}\right) \rho_{\mathrm{c}} \mathrm \ {g}\)

\(\mathrm{v}_{1}+\frac{\mathrm{v}_{2} \rho_{\mathrm{o}}}{\rho_{\mathrm{w}}}=\left(\mathrm{v}_{1}+\mathrm{v}_{2}\right) \frac{\rho_{\mathrm{c}}}{\rho_{\mathrm{w}}}\)

\(=\mathrm{v}_{1}+0.8 \ \mathrm{v}_{2}=0.9 \ \mathrm{v}_{1}+0.9 \ \mathrm{v}_{2}\)

\(=0.1 \ \mathrm{v}_{1}=0.1 \ \mathrm{v}_{2}\)

\(\mathrm{v}_{1}: \mathrm{v}_{2}=1: 1\)