The rate of change of momentum of an object is proportional toI. Mass of the body II. Velocity of the bodyIII. Net force applied on the body IV. None of these

Break Down the Problem

1. Identify the concepts involved in momentum and the factors affecting its change.
2. Examine the relationship between momentum, mass, velocity, and net force.

Relevant Concepts

1. The momentum $p$ of an object is defined as: $p = m \cdot v$ where $m$ is the mass and $v$ is the velocity.
2. The rate of change of momentum is related to net force $F$ applied according to Newton’s second law: $F = \frac{dp}{dt}$ This means that the rate of change of momentum is equal to the net force applied.

Analysis and Detail

1. Mass of the body: Although mass influences momentum, the rate of change of momentum being solely proportional to mass is misleading because changes in momentum occur due to external forces.
2. Velocity of the body: While velocity affects the magnitude of momentum, it doesn't directly correlate to the rate of change of momentum.
3. Net force applied on the body: According to Newton’s second law, the rate of change of momentum is directly proportional to the net force acting on the body.

Verify and Summarize

The fundamental concept here is that net force is what changes momentum, rather than mass or velocity in isolation. Therefore, the correct option must reflect this understanding.

Final Answer

The rate of change of momentum of an object is proportional to III. Net force applied on the body.