# A wooden block floating in a bucket of water has 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 : Option 1) $0.5$ Option 2) $0.8$ Option 3) $0.6$ Option 4) $0.7$

$\\P_{block}=\frac{4}{5}p_w\\\:\Rightarrow\frac{4}{5}VP_{w}g=mg-------(1)$

$\Rightarrow\frac{V}{2}P_{w}g+\frac{V}{2}p^{'}g=mg=\frac{4}{5}VP_{w}g$

$\Rightarrow\frac{1}{2}P_{w}+\frac{p^{'}}{2}=\frac{4}{5}P_{w}$

$\\\Rightarrow\frac{p^{'}}{2}=\left [ \frac{4}{5}-\frac{1}{2} \right ]P_{w}\\\:\:\:p^{'}=\frac{6}{10}P_{w}\\\:\:\:\Rightarrow P^{'}=\frac{3}{5}P_{w}=0.6P_{w}$

Option 1)

$0.5$

Option 2)

$0.8$

Option 3)

$0.6$

Option 4)

$0.7$

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