Question

a log of wood floats in water with 1/5 of its volume above the surface. what is the density of wood

Answer 1

800kg/m^3 is the correct answer

Answer 2

Answer:

The density of wood is 0.8 g/cm³.

Explanation:

Given the problem is -

• There is a log of wood floating in the water.
• 1/5 portion of the log is above the surface of the water.

W have to find the density of the wood.

We know that for any floating body -

Weight of the body = Force of the Up thrust

or,

$V_B \rho_Bg = V_{in}\rho_wg$

where,

$V_B$ = Volume of the body

$\rho_B$ = density of the body

$\rho_w$ = density of the water = 1 g/cm³

$V_{in}$ = Volume inside the water = $\frac{4}{5} V_B$

Putting the values -

$V_B\rho_Bg = V_{in}\rho_wg\\\\V_B\rho_B = \frac{4}{5} V_B\rho_w\\\\\rho_B = \frac{4}{5}\rho_w \\\\\rho_B = 0.8 \ g/cm^3$

The density of wood is 0.8 g/cm³.

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