Question

A cube of wood of side 10cm floats in water with 4.5cm of its depth below the surface, and with its sides vertical. What is the density of wood?

Answer 1

Hope you understand the calculations yourself

Answer 2

Answer:

The density of the cube is $\rho_{c}=450\ kg/m^3$

Explanation:

The side of the wood is a=10 cm

The length of the vertical side of the cube immersed in the water is l=4.5 cm

The density of the water is $\rho_{w}=1000 kg/m^3$

The volume of water displaced by the cube is

$V_{w}=10\times 10^{-2}\times 10\times 10^{-2}\times 4.5\times 10^{-2}\\V_{w}=450\ m^3$

The volume of the cube is,

$V_{c}=10\times 10^{-2}\times 10\times 10^{-2}\times 10\times 10^{-2}\\V_{c}=1000\times 10^{-6}\ m^3$

Let the density of the cube be $\rho_{c}$

We know that the weight of the cube is equal to the weight water displaced by the cube so that it can float

$\rho _{c} V_{c} g=\rho_{w} V_{w} g\\\rho_{c}\times 1000\times 10^{-6}\times 9.8 =1000\times 450\times 10^{-6}\times 9.8\\\rho_{c}=\dfrac{1000\times 450\times 10^{-6}\times 9.8}{1000\times 10^{-6}\times 9.8 }\\\rho_{c}=450\ kg/m^3$