Final answer:
The claim is true as an object's momentum stays constant unless acted on by an unbalanced external force, in accordance with Newton's first law of motion and the principle that net force equals the rate of change of momentum, as per Newton's second law.
Step-by-step explanation:
The statement that the momentum of an object remains the same unless an unbalanced force acts on it is true. According to Newton's first law, also known as the law of inertia, a body at rest will stay at rest, and a body in motion will continue to move at a constant velocity in a straight line unless compelled to change by the action of an external force. This external force is related to the rate of change of momentum, as depicted by Newton's second law, which can be expressed as F = dp/dt, where F represents the net force, p the momentum, and t the time.
When the momentum of an object increases with respect to time, it implies that a net force is acting on it, since the net force is equal to the rate of change of the momentum, not the product of the momentum and the time interval. Therefore, statement 'b' suggesting that the net force is zero because it is the product of the momentum and the time interval is incorrect. Furthermore, the conservation of momentum occurs when there is no net external force acting on the system, as stated in Newton's third law, which describes action and reaction forces acting in equal magnitudes but opposite directions.