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Q.

A cubical block of wood of specific gravity 0.5 and chunk of concrete of specific gravity 2.5 are fastened together. The ratio of mass of concrete to the mass of wood which makes the combination to float with its entire volume submerged in water is

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a

$\frac{5}{3}$

b

$\frac{6}{5}$

c

$\frac{5}{2}$

d

$\frac{4}{3}$

answer is A.

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Detailed Solution

Let $m_{1}$ = mass of concrete and
$m_{2}$ = mass of wood
From law of floatation,
Weight = upthrust

$(m_{1} + m_{2}) g = (\frac{m_{1}}{2.5} + \frac{m_{2}}{0.5}) (1) (g)$

$\Rightarrow \frac{m_{1}}{m_{2}} + 1 = \frac{2}{5} \frac{m_{1}}{m_{2}} + 2$

$\Rightarrow \frac{3}{5} \frac{m_{1}}{m_{2}} = 1 \Rightarrow \frac{m_{1}}{m_{2}} = \frac{5}{3}$

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A cubical block of wood of specific gravity 0.5 and chunk of concrete of specific gravity 2.5 are fastened together. The ratio of mass of concrete to the mass of wood which makes the combination to float with its entire volume submerged in water is