A cubical block of wood of specific gravity 0.5 and a chunk of concrete of specific gravity 2.5 are

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9-1.Fluid Mechanics

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

A

$1/5$

B

$1/3$

C

$3/5$

D

$2/5$

Solution

Let the mass of wood and concrete be $M$ and

$m$ respectively. Then

$\frac{M}{0.5}+\frac{m}{2.5}=(M+m)$

$\mathrm{Or}$ $M \left(\frac{1}{0.5}-1\right)=m\left(1-\frac{1}{2.5}\right)$

$\mathbf{o r}$ $M=m\left(\frac{1.5}{2.5}\right)=m\left(\frac{3}{5}\right)$

$\therefore$ $\frac{M}{\operatorname{m}}=\frac{3}{5}$

Standard 11

Physics

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