The ax consists of a wooden handle and a stone adze. The density of the wood is 600 kg per meter and the weight

The ax consists of a wooden handle and a stone adze. The density of the wood is 600 kg per meter and the weight of the handle made from it is one-sixth of the mass of the entire ax and the volume of the handle is half of the volume of the entire ax. find the density of the stone from which the adze is made.

Given:

ro1 = 600 kg / m ^ 3 is the density of the tree from which the ax handle is made;

m1 = m / 6 is the mass of the handle in relation to the mass of the ax;

V1 = V / 2 – the volume of the handle in relation to the volume of the ax.

It is required to determine the density of the stone ro2 (kg / m ^ 3), from which the adze is made.

The mass of the wooden handle is:

m1 = ro1 * V1 = ro1 * V / 2. = m / 6, hence:

m = 3 * ro1 * V.

The mass of a stone tesla is:

m2 = 5 * m / 6 = 5 * 3 * ro1 * V / 6 = 5 * ro1 * V / 3.

taking into account that m2 = ro2 * V / 2, then:

ro2 * V / 2 = 5 * ro1 * V / 3;

ro2 / 2 = 5 * ro1 / 3, hence:

ro2 = 10 * ro1 / 3 = 10 * 600/3 = 10 * 200 = 2000 kg / m ^ 3.

Answer: the density of a stone tesla is 2000 kg / m ^ 3.