First slide

Fluid statics

Question

A cubical block of wood specific gravity 0.5 and 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

Moderate

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
$\frac{M}{0 \cdot 5} + \frac{m}{2 \cdot 5} = (M + m) M [\frac{1}{0 \cdot 5} - 1] = m [1 - \frac{1}{2 \cdot 5}] M = m (\frac{1 \cdot 5}{2 \cdot 5}) or \frac{M}{m} = \frac{3}{5}$

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