Question

question 2 (1 point) listen what happens to the density of an object when it is cut in half? a) the mass and volume decrease, and the density decreases. b) the mass and volume increase, but the density remains the same. c) the mass and volume decrease, but the density increases. d) the mass and volume decrease, but the density remains the same. e) the mass and volume increase, and the density increases.

Explanation:

Density is defined as $
ho = \frac{m}{V}$, where $m$ is mass and $V$ is volume. When an object is cut in half, its mass ($m$) and volume ($V$) both decrease by half (since the amount of matter and the space it occupies are both halved). So the new mass $m'=\frac{m}{2}$ and new volume $V'=\frac{V}{2}$. Then the new density $
ho'=\frac{m'}{V'}=\frac{\frac{m}{2}}{\frac{V}{2}}=\frac{m}{V}=
ho$. So mass and volume decrease, but density remains the same. Option d states this correctly. Options a (density decreases), b (mass/volume increase), c (density increases), e (mass/volume increase and density increases) are incorrect.

Answer:

d) The mass and volume decrease, but the density remains the same.