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

 

Answers (1)

\\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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