This question asks us to identify the correct statements regarding two core concepts in physics: the relationship between mass and inertia, and the principle of momentum conservation in an isolated system.

Mass and Inertia Explained

Statement I says: "The mass of an object is a measure of its inertia."

• Mass is a fundamental property of an object that quantifies the amount of matter it contains. It is a scalar quantity and is constant for a specific object, regardless of its location or state of motion.
• Inertia is an inherent property of an object that describes its resistance to changes in its state of motion. Simply put, an object at rest tends to stay at rest, and an object in motion tends to continue moving at a constant velocity (constant speed in a straight line), unless an external force acts upon it. This concept is a direct consequence of Newton's first law of motion.
• The greater the mass of an object, the more difficult it is to change its state of motion. For example, it requires much more force to accelerate a large truck than a small car from rest. This resistance to change in motion is precisely what inertia represents.

Therefore, mass serves as a quantitative measure of an object's inertia. Objects with greater mass exhibit greater inertia. Thus, Statement I is correct.

Momentum Conservation Principle

Statement II says: "In an isolated system the total momentum remains conserved."

• Momentum is a vector quantity that describes the "quantity of motion" an object possesses. It is calculated as the product of an object's mass and its velocity, represented by the formula \(p = mv\), where \(p\) is momentum, \(m\) is mass, and \(v\) is velocity.
• An isolated system is a collection of objects where no external forces act on any part of the system. This means that any forces present are internal forces, acting only between the objects within the system. External forces from outside the system are either absent or cancel each other out, resulting in a net external force of zero.
• The Law of Conservation of Momentum is a fundamental principle stating that in an isolated system, the total momentum of the system remains constant over time. This means that if no net external force acts on the system, the sum of the momenta of all objects within the system before an event (like a collision or an explosion) will be equal to the sum of their momenta after the event. Mathematically, for an isolated system, \(\Sigma p_{\text{initial}} = \Sigma p_{\text{final}}\).
• For instance, when two billiard balls collide on a frictionless table (approximating an isolated system), the total momentum of the two balls before the collision is the same as their total momentum after the collision, even though the individual momenta of the balls may change.

This principle is a cornerstone of physics and holds true universally for isolated systems. Thus, Statement II is correct.

Overall Correctness of Statements

Based on the detailed analysis, both statements are fundamental and correct principles of classical mechanics:

• Statement I correctly defines mass as the measure of inertia.
• Statement II correctly states the Law of Conservation of Momentum for an isolated system.

Since both Statement I and Statement II are correct, the option stating "Both I and II" is the accurate choice.