Certainly! Let's solve this step-by-step.
To determine the most plausible value for the density of an object from the given choices, we need to understand the units typically used for density and discard the values that don't match these units. Density is usually expressed in terms of mass per unit volume.
1. Understanding the Units of Density:
The formula for density is given by [tex]\( D = \frac{m}{v} \)[/tex], where:
- [tex]\( m \)[/tex] is the mass, often measured in grams (g).
- [tex]\( v \)[/tex] is the volume, often measured in cubic centimeters ([tex]\(cm^3\)[/tex]).
Therefore, the unit of density is typically [tex]\( g/cm^3 \)[/tex].
2. Assessing the Given Choices:
Now let's evaluate each of the given choices in terms of whether they are plausible representations of density:
- [tex]\(-1 \, g/cm^3\)[/tex]: This value is in the correct units of density but is negative. In practical scenarios, density should be a positive quantity because mass and volume are both positive quantities.
- [tex]\(4 \, m/s\)[/tex]: This unit represents speed (meters per second) and not density. Certainly, it can't represent the density of an object.
- [tex]\(-3 \, m/s\)[/tex]: Similar to the previous option, this unit also represents speed and not density. In addition, it is negative, which further invalidates it.
- [tex]\(6 \, g/cm^3\)[/tex]: This value is in the correct units of density (grams per cubic centimeter) and is positive, making it a reasonable and plausible value.
3. Conclusion:
Among the choices, the value that makes logical sense as a representation of density, both in terms of the units and being a positive value, is:
[tex]\[
6 \, g/cm^3
\][/tex]
Thus, the most plausible value representing the density of the object is [tex]\( \boxed{6 \, g/cm^3} \)[/tex].
