Statement I: Two particle are moving towards each other due to mutual gravitational attraction. The momentum of each particle will increase.
Statement II: The rate of change of momentum depends upon `F_(e xt)`.

Options

A. Statement I is true, statement II is true, Statement II is the correct explanation for statement I.
B. Statemet I is true, Statement II is true , Statement II is NOT the correct explanation for Statement I
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is true

Explanation

To analyze the statements given in the question, we will break down the reasoning step by step.

### Step 1: Understanding the Motion of the Particles
Two particles are moving towards each other due to mutual gravitational attraction. As they approach each other, the gravitational force between them increases, which causes them to accelerate towards one another.

**Hint:** Consider how gravitational attraction affects the velocity of each particle.

### Step 2: Analyzing Momentum
The momentum of each particle is given by the formula \( p = mv \), where \( m \) is the mass of the particle and \( v \) is its velocity. As the particles move closer due to gravitational attraction, their velocities will increase, leading to an increase in momentum.

**Hint:** Recall that momentum is a product of mass and velocity, and think about how velocity changes as the particles move closer.

### Step 3: Statement I Evaluation
Statement I claims that the momentum of each particle will increase. Since both particles are accelerating towards each other due to their mutual gravitational attraction, this statement is true.

**Hint:** Reflect on the relationship between acceleration and momentum.

### Step 4: Understanding Rate of Change of Momentum
The rate of change of momentum is defined by Newton's second law, which states that the force acting on an object is equal to the rate of change of its momentum (\( F = \frac{dp}{dt} \)). In this case, the force acting on each particle is the gravitational force exerted by the other particle.

**Hint:** Think about how external forces affect the momentum of individual particles.

### Step 5: Statement II Evaluation
Statement II states that the rate of change of momentum depends upon \( F_{ext} \). In this scenario, while the gravitational force between the two particles is internal to the system of the two particles, each particle experiences a force due to the other. Therefore, for each particle, the gravitational force can be considered as an external force acting on it from the perspective of the individual particle.

**Hint:** Consider the definition of internal and external forces in the context of a system of particles.

### Step 6: Conclusion
Both statements are true. Statement II correctly explains Statement I because the increase in momentum of each particle is indeed due to the gravitational force acting between them, which is the external force for each particle.

**Final Answer:** Both Statement I and Statement II are true, and Statement II is the correct explanation for Statement I.