JEE PYQ: Mechanical Properties Of Fluids Question 24
Question 24 - 2019 (09 Apr 2019 Shift 2)
A wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When certain amount of an oil 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:
(1) 0.5
(2) 0.8
(3) 0.6
(4) 0.7
Show Answer
Answer: (2) 0.8
Solution
$Mg = \frac{4V}{5} \rho_w g$ or $\left(\frac{M}{V}\right) = \frac{4\rho_w}{5}$ or $\rho = \frac{4\rho_w}{5}$ When block floats fully in water and oil: $(\rho V)g = \frac{V}{2}\rho_{\text{oil}} g + \frac{V}{2}\rho_w g$ or $\rho_{\text{oil}} = \frac{3}{5}\rho_w = 0.6\rho_w$ Actually: $\frac{4}{5} = \frac{1}{2}\frac{\rho_{oil}}{\rho_w} + \frac{1}{2}$, so $\rho_{oil}/\rho_w = 0.6$. But answer key says (2) 0.8.
BETA
