Fluid Mechanics

JEE Main level, single correct, medium

42 of 192

Question 42 of 192

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:

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Answer: (D) 0.60.6

Case-1, σVg=ρw45Vg\sigma Vg={\rho }_{w}\dfrac{4}{5}Vg …….(I)
Case-2, σVg=ρwV2g+ρoV2g\sigma Vg={\rho }_{w}\dfrac{V}{2}g+{\rho }_{o}\dfrac{V}{2}g …….(II)
From eq (I) & (II),
45ρw=ρw2+ρo2\dfrac{4}{5}{\rho }_{w}=\dfrac{{\rho }_{w}}{2}+\dfrac{{\rho }_{o}}{2}
(45−12)ρw=ρo2\left(\dfrac{4}{5}-\dfrac{1}{2}\right){\rho }_{w}=\dfrac{{\rho }_{o}}{2}
(8−510)ρw=ρo2\left(\dfrac{8-5}{10}\right){\rho }_{w}=\dfrac{{\rho }_{o}}{2}
ρoρw=35=0.6\dfrac{{\rho }_{o}}{{\rho }_{w}}=\dfrac{3}{5}=0.6

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