In classical mechanics, linear momentum of a body is defined as the product of which two physical quantities associated with the motion of the body?

Introduction / Context:
Momentum is a central concept in mechanics that helps describe how difficult it is to change the motion of a moving body. It appears in Newton second law in its original form and is conserved in many collision and explosion problems. This question checks whether you know the basic definition of linear momentum in terms of simple measurable quantities like mass and velocity.

Given Data / Assumptions:
- We are dealing with linear momentum of a body moving in a straight line.- The definition should involve simple mechanical quantities.- Standard definitions from introductory physics are assumed.

Concept / Approach:
Linear momentum p of an object is defined as the product of its mass m and its velocity v. In symbolic form, p = m * v. Momentum is a vector quantity because velocity is a vector; it has both magnitude and direction. Momentum combines how much matter is moving (mass) with how fast and in what direction it is moving (velocity). This makes momentum particularly useful when analysing collisions, as total momentum of an isolated system is conserved. Inertia, force, and acceleration are related ideas but do not directly form the definition.

Step-by-Step Solution:
1. Recall that momentum symbol p is defined as p = m * v.2. Identify that mass m is a scalar quantity measuring the amount of matter in the body.3. Identify that velocity v is a vector describing both the speed and direction of motion.4. Recognise that inertia is a qualitative property related to mass but not used directly in the momentum formula.5. Recognise that force and acceleration have their own relation F = m * a and do not define momentum.6. Therefore, the product of mass and velocity is the correct expression for linear momentum.

Verification / Alternative check:
Newton second law in its general form can be written as net force equals rate of change of momentum. If momentum were defined as some other combination, this law would not match the observed proportionality between force, mass, and acceleration. Using p = m * v gives F = m * a for constant mass, which matches experiments. This consistency across laws confirms that momentum must be the product of mass and velocity.

Why Other Options Are Wrong:
- Mass and inertia: Inertia is essentially the resistance to change in motion and is closely related to mass, so mass times inertia is not a standard physical quantity.- Mass and force: Their product would have units inconsistent with momentum and does not appear as a basic definition.- Mass and acceleration: The product m * a gives force, according to Newton second law, not momentum.

Common Pitfalls:
Because mass times acceleration appears frequently in problems, students can mistakenly associate it with momentum. Remember that momentum tells you about the current state of motion, while force tells you about the rate of change of that state. Keeping track of dimensions and units can also help: momentum has units of kilogram metre per second, while force has units of newton, which is kilogram metre per second squared.

Final Answer:
Linear momentum of a body is defined as the product of its mass and its velocity.