A wooden block floats in water with two-third of its volume submerged.

(a) Calculate the density of wood.
(b) When the same block is placed on oil, three-quarter of its volume is immersed in oil. Calculate the density of oil.

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Solution

Let D be the density of wood

Density of wood / Density of Water = Part of block submerged / Total Part

$D over 1 equals fraction numerator begin display style fraction numerator 2 V over denominator 3 end fraction end style over denominator V end fraction$

= 0.67 $g / c m^{3}$

b)Again ,
$fraction numerator begin display style fraction numerator 3 V over denominator 4 end fraction end style over denominator V end fraction equals fraction numerator 0.67 over denominator D end fraction 3 over 4 equals fraction numerator 0.67 over denominator D end fraction$
D = 0.89 $g / c m^{3}$

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