Question

A square block of steel with volume 10 cm3 and mass of 75 g is cut precisely in half. The density of the two smaller pieces is now...
a. the same as the original density.
b. one-half the original density.
c. two times the original density.
d. one-fourth the original density.

Answer 1

Answer:

a. the same as the original density.

Explanation:

The density of a material depends only on the properties of the material, so if a block of steel is cut in a half, it is still made of the same material (steel), so it still has the same density.

We can verify it by doing some calculations. In fact, the initial density of the block of steel is given by the ratio between its mass (75 g) and its volume (10 cm^3):

$d=\frac{m}{V}=\frac{75 g}{10 cm^3}=7.5 g/cm^3$

When the block is cut in a half, its mass becomes half:

$m' = \frac{m}{2}=\frac{75 g}{2}=37.5 g$

and its volume also becomes half:

$V'=\frac{V}{2}=\frac{10 cm^3}{2}=5 cm^3$

So the new density is

$d'=\frac{m'}{V'}=\frac{37.5 g}{5 cm^3}=7.5 g/cm^3$

So, the density has not changed.

Answer 2

A. Density only depends on the substance. It doesn't matter whether you have a little chip of it or a supertanker full of it ... the density doesn't change.