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JEE Main 20199 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
9 April
Shift
Evening Shift
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2019 · 9 April · Evening Shift · Physics · Mechanical Properties of Fluids

A wooden block floating in a bucket of water has (4)/(5) of its...

A wooden block floating in a bucket of water has 45\dfrac{4}{5} 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:

Options

  1. A0.80.8
  2. B0.70.7
  3. C0.50.5
  4. D0.60.6

Correct answer

D. 0.60.6

Step-by-step solution

Case-1, \sigmaVg=ρw45Vg\sigmaVg = {ρ}_{w}\dfrac{4}{5}Vg …….(I)
Case-2, \sigmaVg=ρwV2g+ρoV2g\sigmaVg = {ρ}_{w}\dfrac{V}{2}g + {ρ}_{o}\dfrac{V}{2}g …….(II)
From eq (I) & (II),
45ρw=ρw2+ρo2\dfrac{4}{5}{ρ}_{w} = \dfrac{{ρ}_{w}}{2} + \dfrac{{ρ}_{o}}{2}
\left(\dfrac{4}{5} - \dfrac{1}{2}\right){ρ}_{w} = \dfrac{{ρ}_{o}}{2}<br/>(8−510)ρw=ρo2<br/>\left(\dfrac{8 - 5}{10}\right){ρ}_{w} = \dfrac{{ρ}_{o}}{2}
ρoρw=35=0.6\dfrac{{ρ}_{o}}{{ρ}_{w}} = \dfrac{3}{5} = 0.6
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