Step 1: Analyze the definition provided in the question.
The question asks to identify the force of mutual attraction between two objects that exists "by virtue of their masses." This means the force exists because the objects have mass, and its strength depends on their masses.
Step 2: Compare this definition with the fundamental forces of nature.
There are four fundamental forces:
1. Gravitational force: An attractive force that acts between any two objects with mass. The strength of the force is proportional to the product of the masses.
2. Electromagnetic force: Acts between electrically charged particles. It is not directly dependent on mass.
3. Strong nuclear force: Holds the nucleus of an atom together, acting between protons and neutrons. It is extremely short-range and is not a function of the total mass of an object.
4. Weak nuclear force: Responsible for radioactive decay processes. It is also a very short-range force.
Step 3: Conclude the correct identification.
The definition given in the question perfectly matches the description of the gravitational force. Newton's Law of Universal Gravitation, $F = G\frac{m_1 m_2}{r^2}$, explicitly states that this force is due to the masses ($m_1, m_2$) of the objects.