In mechanics, linear momentum of a body is directly related to which properties of matter, according to the definition p = m * v?

Introduction / Context:
Linear momentum is a basic concept in mechanics that describes the quantity of motion of a body. It plays a central role in collision problems, conservation laws and dynamics. The formal definition links momentum to both mass and velocity. This question checks whether you can correctly identify which properties of matter momentum depends on, based on the standard formula.

Given Data / Assumptions:

• Linear momentum p is defined in classical mechanics as p = m * v.
• Here m is the mass of the body and v is its velocity.
• Mass is a measure of how much matter a body contains.
• Velocity is a vector quantity describing speed and direction of motion.

Concept / Approach:
The equation p = m * v shows that momentum is the product of mass and velocity. If either mass or velocity increases, the magnitude of momentum increases, assuming the other quantity stays the same. This means momentum depends on both how much matter is moving and how fast it is moving. A heavy object moving slowly and a lighter object moving fast can have the same momentum if m * v is equal. Therefore, any answer that includes only mass or only velocity is incomplete; the correct choice is that momentum is related to both mass and velocity.

Step-by-Step Solution:
Step 1: Write the definition of linear momentum: p = m * v.Step 2: Identify that m, the mass, is one factor in the product.Step 3: Identify that v, the velocity, is the other factor in the product.Step 4: Recognise that if mass increases while velocity remains constant, momentum increases proportionally.Step 5: Recognise that if velocity increases while mass remains constant, momentum also increases proportionally.Step 6: Conclude that momentum is directly related to both mass and velocity, not just one of them.

Verification / Alternative check:
Consider two objects: a truck of mass 4000 kg moving at 5 m/s and a car of mass 1000 kg moving at 20 m/s. The truck momentum is 4000 * 5 = 20,000 kg m/s, while the car momentum is 1000 * 20 = 20,000 kg m/s. Even though the truck has more mass and the car has more velocity, their momenta are equal because momentum depends on both properties. This practical example confirms that neither mass nor velocity alone determines momentum.

Why Other Options Are Wrong:
Option A, mass only, ignores the fact that a stationary object with large mass has zero momentum because its velocity is zero. Option B, velocity only, ignores that a very light object moving fast may have less momentum than a heavier object moving slowly. Option D claims that momentum is related to none of the listed properties, which directly contradicts the definition.

Common Pitfalls:
Students may sometimes think of momentum as simply heaviness in motion and focus only on mass, or they may focus only on speed. Others forget the vector nature of momentum and treat it as a scalar. To avoid these mistakes, always refer back to the precise definition p = m * v and remember that both mass and velocity contribute to the magnitude and direction of momentum.

Final Answer:
Momentum is directly related to both mass and velocity, since p = m * v.