A wooden block floating in a bucket of water | vedclass

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(B) Let $V$ be the total volume of the wooden block and $\sigma$ be its density. Let $\rho$ be the density of water.Initially,the block floats in wate

Vedclass · Accepted Answer

$3/5$

Vedclass · Answer

(B) Let $V$ be the total volume of the wooden block and $\sigma$ be its density. Let $\rho$ be the density of water.Initially,the block floats in water with $(4/5)V$ submerged. By the law of floatation,the weight of the block equals the buoyant force:$V \sigma g = (4/5)V \rho g$$\sigma = (4/5) \rho$ ...$(i)$When oil is poured,the block is submerged such that half its volume $(V/2)$ is in water and half $(V/2)$ is in oil. Let $\rho_o$ be the density of oil.The total buoyant force equals the weight of the block:$V \sigma g = (V/2) \rho g + (V/2) \rho_o g$Substituting $\sigma = (4/5) \rho$ from $(i)$:$(4/5) V \rho = (1/2) V \rho + (1/2) V \rho_o$Dividing by $V$ and multiplying by $2$:$(8/5) \rho = \rho + \rho_o$$\rho_o = (8/5 - 1) \rho = (3/5) \rho$Thus,the relative density of oil with respect to water is $3/5$.

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