Question

A wooden block cross section diameter 20cm,and 4m long floats in water what part of volume is above water.If density of wooden block is 700kg/m*m*m and of water is 1000kg/m*m*m

Answer 1

Answer on Question #43052 – Math – Other

A wooden block cross section diameter $20\mathrm{cm}$, and $4\mathrm{m}$ long floats in water what part of volume is above water. If density of wooden block is $700\mathrm{kg/m*m*m}$ and of water is $1000\mathrm{kg/m*m*m}$

Solution.

Let $h$ be the altitude of the block over the water. The volume of the under the water part of the block is $V_{0} = \frac{\pi \cdot 0.2^{2}}{4} \cdot 4 = 0.04\pi \mathrm{m}^{3}$. The volume of all block is $V = \frac{\pi \cdot 0.2^{2}}{4} \cdot (4 + h)$. By Archimed's principle

$$\rho_{\text{water}} V_{0} g = \rho_{\text{wood}} V g \text{ (buoyancy = gravity)}.$$

Hence, $\frac{V}{V_0} = \frac{\rho_{\text{water}}}{\rho_{\text{wood}}}$ or $\frac{4 + h}{4} = \frac{10}{7}$, so $h = \frac{12}{7} \approx 1.714 \, \text{m}$.

Answer: $h = \frac{12}{7} \approx 1.714 \, \text{m}$

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