Iron and aluminum rods have the same cross-sections and which weight is longer?

Given:

ro1 = 7800 kilograms per cubic meter – the density of iron;

ro2 = 2700 kilograms per cubic meter – the density of aluminum;

s1 = s2 = s – sections of both rods are the same;

m1 = m2 = m – the mass of both rods is the same.

It is required to determine which of the rods is longer.

Since it is not specified in the problem statement, we assume that the rods have the geometric shape of a cylinder.

Then, the length of the iron rod will be equal to:

l1 = V1 / s1 = m1 / (ro1 * s1) = m / (ro1 * s) = k / ro1 = k / 7800, where k = m / s.

The length of the aluminum rod will be:

l2 = V2 / s2 = m2 / (ro2 * s2) = m / (ro2 * s) = k / ro1 = k / 2700.

Since l2> l1 (k / 2700> k / 7800), the aluminum rod will be long.

Answer: The aluminum rod is longer.