Two cubical blocks identical in dimensions fl | vedclass

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(A) According to the law of floatation,for a body floating in a liquid,the weight of the body is equal to the weight of the liquid displaced.Let $V$ b

Vedclass · Accepted Answer

$2:3$

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(A) According to the law of floatation,for a body floating in a liquid,the weight of the body is equal to the weight of the liquid displaced.Let $V$ be the volume of each cubical block and $ho_w$ be the density of water.For the $1$st block: Weight of block = Weight of displaced water $\implies V \cdot ho_1 \cdot g = (V/2) \cdot ho_w \cdot g \implies ho_1 = ho_w / 2$.For the $2$nd block: Weight of block = Weight of displaced water $\implies V \cdot ho_2 \cdot g = (3V/4) \cdot ho_w \cdot g \implies ho_2 = 3ho_w / 4$.The ratio of densities of the blocks is $ho_1 / ho_2 = (ho_w / 2) / (3ho_w / 4) = (1/2) 	imes (4/3) = 2/3$.

Two cubical blocks identical in dimensions float in water in such a way that the $1$st block floats with half part immersed in water and the $2$nd block floats with $3/4$ of its volume inside the water. The ratio of densities of the blocks is ..........

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