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 wood to the mass of concrete which makes the combination to float with entire volume of the combination submerged in water is

Engineering

Physics

Statics

Question

1/5

2/5

3/5

1/3

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Let volume of block = V₁
Volume of concrete = V₂
∴ Displaced volume of water = (V₁ + V₂)
Now, weight of the combination = Bouyant force
∴ 0.5 × V₁g + 0.25 × V₂g = 1 × (V₁ + V₂) g

$∴ \frac{V_{1}}{V_{2}} = \frac{3}{1} ∴ \frac{m_{1}}{m_{2}} = \frac{0.5 \times V_{1}}{0.25 \times V_{2}} = 3 / 5$ .

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