Question

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

• A. 8:9
• B. 5:4
• C. 9:10
• D. 1:1

Hint:

Floating objects distribute their volume based on density ratios of the fluids they are immersed in.

Answer 1

The Correct Option is D

Step 1: Define variables.
Let \( V_1 \) be the volume immersed in water and \( V_2 \) be the volume immersed in oil.
Step 2: Equilibrium condition.
\[ V_1 \rho_w g + V_2 \rho_o g = (V_1 + V_2) \rho_{{ice}} g \] 
Step 3: Solve for ratio.
\[ V_1 + 0.8 V_2 = 0.9 (V_1 + V_2) \] \[ 0.1 V_1 = 0.1 V_2 \Rightarrow V_1 : V_2 = 1:1 \] The ratio of volumes immersed in water to oil is 1:1.