Q 11-09-072JEE MainJEE Main 2024 (8 Apr, Shift 2)Easy
A cube of ice floats partly in water and partly in kerosene oil (kerosene forms a layer above the water). The ratio of volume of ice immersed in water to that in kerosene oil is (specific gravity of kerosene oil $= 0.8$, specific gravity of ice $= 0.9$):
Answer: (A) $1:1$
The whole cube is submerged, with $V_w$ in water and $V_k$ in kerosene. Weight = total buoyancy:
$$0.9(V_w + V_k) = 1.0\,V_w + 0.8\,V_k \;\Rightarrow\; 0.1V_k = 0.1V_w$$
$$V_w : V_k = 1 : 1$$
Solution by Sreeraj P, M.Sc Physics