A cube of ice floats partly in water and partly in kerosene oil....

A cube of ice floats partly in water and partly in kerosene oil. The radio 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)

A cube of ice floats partly in water and partly in kerosene oil. The radio of volume of ice immersed in water to that

Options

A $8: 9$
B $5: 4$
C $9: 10$
D $1: 1$

Correct answer

D. $1: 1$

Step-by-step solution

Let

V_1

be, the volume immersed in water.

V_2

be the volume immersed in oil. In equilibrium condition,

v_1 \rho_w g+v_2 \rho_0 g=\left(v_1+v_2\right) \rho_e gv_1+\frac{v_2 \rho_0}{\rho_w}=\left(v_1+v_2\right) \frac{\rho_c}{\rho_w}\Rightarrow v_1+0.8 v_2=0.9 v_1+0.9 v_2 \Rightarrow 0.1 v_1=0.1 v_2\Rightarrow v_1: v_2=1: 1

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