Q 11-09-146JEE MainJEE Main 2019 (9 Apr, Shift 2)Easy
A wooden block floating in a bucket of water has $\frac45$ of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is
Answer: (D) $0.6$
From the first case, the block's relative density is $\frac45 = 0.8$.
In the second case the weight is balanced by buoyancy from both liquids:
$$V(0.8) = \frac V2(1) + \frac V2\rho_{oil} \Rightarrow \rho_{oil} = 2(0.8 - 0.5) = 0.6$$
Solution by Sreeraj P, M.Sc Physics