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Archimedes' Principle

A block of wo...

Question

A block of wood of length $40 c m$ and area of cross section $15 {c m}^{2}$ floats in water with $3 / 8$ of its length above water. What is the density of wood? (density of water $= 1 g {c m}^{- 3}$ )

0.256 g {c m}^{- 3}

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0.526 g {c m}^{- 3}

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0.625 g {c m}^{- 3}

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0.650 g {c m}^{- 3}

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Solution

The correct option is C $0.625 g {c m}^{- 3}$
Relative density = $\frac{V o l u m e o f b o d y i m m e r s e d}{T o t a l v o l u m e o f b o d y}$
Relative = $1 - \frac{3}{8} = \frac{5}{8}$
So, density of wood $= \frac{5}{8} \times d e n s i t y o f w a t e r$
$= 0.625 \times 1 g / c c$
density $= 0.625 g / c c$

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