Which law of Newton provides a quantitative definition of force?

The correct answer is Second law of motion.

Newton's laws of motion are three fundamental principles that describe how objects move and interact with forces. Among these, only one provides a quantitative (mathematical/measurable) definition of force — and that is Newton's Second Law of Motion.

Let's understand why each law is or isn't the answer:

First Law of Motion (Law of Inertia):
This law states that an object remains at rest or in uniform motion unless acted upon by an external force. While it introduces the concept of force qualitatively (force is what changes the state of motion), it does not give a mathematical formula to measure or calculate force. So, it is not a quantitative definition.

Second Law of Motion:
This law states that the rate of change of momentum of an object is directly proportional to the net applied force, and the change occurs in the direction of the force. Mathematically:

F=ma

Where:
F = Net force applied on the object (in Newtons, N)
m = Mass of the object (in kg)
a = Acceleration produced (in m/s²)

This equation directly defines force in measurable, numerical terms. It tells us exactly how much force is needed to produce a given acceleration in an object of known mass. This is what makes it a quantitative definition — you can plug in numbers and calculate force precisely.

In terms of momentum (p=mv), the second law can also be expressed as:

F=\frac{dp}{dt}

This confirms that force equals the rate of change of momentum — a precise, calculable, and quantitative relationship.

Third Law of Motion:
This law states that for every action there is an equal and opposite reaction. While it involves forces, it describes the nature of force interactions between two bodies — it does not give a standalone formula to define or calculate the magnitude of force independently.

Universal Law of Gravitation:
This is not one of the three laws of motion. It is a separate law by Newton that describes the gravitational force between two masses. It is not the answer here.

Conclusion:
Newton's Second Law of Motion is the only law that gives a clear, mathematical, and measurable definition of force through the equation F=ma. This is why it is called the quantitative definition of force.