According to Newton second law in momentum form, the rate of change of linear momentum of a body with respect to time is equal to which physical quantity?

Introduction / Context:
Newton second law of motion can be expressed in different but equivalent forms. In its most general form, it states that the net external force on a body equals the rate of change of its linear momentum. This question aims to ensure that you can connect this momentum based definition with the simpler F = m * a version that you often use in basic problems, and identify the correct physical quantity from the options given.

Given Data / Assumptions:
- A body has linear momentum that may change with time.- We consider the time rate of change of this momentum.- Standard Newtonian mechanics is assumed, with constant mass unless stated otherwise.

Concept / Approach:
Linear momentum p is defined as p = m * v. Newton second law in its general form states that the net external force F on a body is equal to the time rate of change of its momentum, that is F = dp / dt. When mass is constant, this simplifies to F = m * dv / dt, which can be written as F = m * a, where a is acceleration. Thus, the quantity that directly equals the rate of change of momentum is net force, not area, pressure, or velocity.

Step-by-Step Solution:
1. Start from the general form of Newton second law: net force F = rate of change of momentum.2. Write this mathematically as F = dp / dt, where p is linear momentum.3. Recognise that dp / dt means the derivative of momentum with respect to time, that is how quickly momentum changes.4. Compare this with the options and note that force is explicitly associated with dp / dt.5. Understand that area and pressure are unrelated geometric and thermodynamic quantities, and velocity is part of momentum but not the rate of change of momentum itself.6. Conclude that the correct answer is force.

Verification / Alternative check:
Consider a constant mass m moving with velocity v. Momentum p = m * v. Differentiating with respect to time gives dp / dt = m * dv / dt = m * a. From experiments, we know that the net external force is proportional to acceleration and equals m * a for constant mass. This means that F and dp / dt have the same value, confirming that force is the rate of change of momentum. Textbooks also define Newton second law explicitly using this relationship.

Why Other Options Are Wrong:
- Area: It measures the extent of a surface in square units and has no direct link to momentum change.- Pressure: It is defined as force per unit area and is a scalar field quantity, not the time derivative of momentum.- Velocity: It is the rate of change of displacement with time, not the rate of change of momentum.

Common Pitfalls:
Some students memorise only the simpler F = m * a form of the second law and forget that it originally referred to momentum. As a result, they may confuse which quantities are being differentiated. Remember that the most general and powerful statement is F equals rate of change of momentum, and everything else is a special case of this. Keeping that in mind will help you answer conceptual questions like this more confidently.

Final Answer:
The rate of change of linear momentum of a body is equal to the net force acting on it.