Question

what objects have a density greater than object g in the graph below?
mass vs. volume of objects e-f

a) e, f, and water only
b) e, f, water, and h
c) water only
d) none of them.
e) h only

Explanation:

Step1: Recall the density formula

Density formula is \(
ho=\frac{m}{V}\). In a mass - volume graph, the slope of the line represents density (\( \text{slope}=\frac{\Delta m}{\Delta V}\)).

Step2: Compare slopes

We need to compare the slopes of the lines for objects \(E\), \(F\), \(G\), \(H\) and water.
For object \(G\), assume two points \((0,0)\) and \((10,6)\) (from the graph), slope \(m_G=\frac{6 - 0}{10-0}=0.6\).
For object \(E\), assume two points \((0,0)\) and \((4,9)\), slope \(m_E=\frac{9 - 0}{4-0}=2.25\).
For object \(F\), assume two points \((0,0)\) and \((6,9)\), slope \(m_F=\frac{9 - 0}{6-0}=1.5\).
For water, assume two points \((0,0)\) and \((10,9)\), slope \(m_{water}=\frac{9 - 0}{10-0}=0.9\).
For object \(H\), assume two points \((0,0)\) and \((10,3)\), slope \(m_H=\frac{3 - 0}{10-0}=0.3\).

Since \(m_E = 2.25>0.6\), \(m_F=1.5 > 0.6\) and \(m_{water}=0.9>0.6\)

Answer:

A. E, F, and water only