Newton's II law of motion connects:

Options

A. Momentum and accelration
B. Change of momentum and velocity
C. Rate of change of momentum and external force
D. Rate of change of force and momentum

Explanation

To solve the question regarding what Newton's II law of motion connects, we can follow these steps:

### Step 1: Understand Newton's Second Law of Motion
Newton's second law of motion states that the rate of change of momentum of an object is directly proportional to the net external force acting on it. This can be expressed mathematically as:

\[ F = \frac{dp}{dt} \]

where \( F \) is the net external force, \( p \) is the momentum, and \( t \) is time.

### Step 2: Define Momentum
Momentum (\( p \)) is defined as the product of the mass (\( m \)) of an object and its velocity (\( v \)). Thus, we can express momentum as:

\[ p = mv \]

### Step 3: Rate of Change of Momentum
The rate of change of momentum can be expressed as:

\[ \frac{dp}{dt} = \frac{d(mv)}{dt} \]

If the mass is constant, this simplifies to:

\[ \frac{dp}{dt} = m \frac{dv}{dt} \]

where \( \frac{dv}{dt} \) is the acceleration (\( a \)) of the object.

### Step 4: Connect to Force
According to Newton's second law, we can relate this to force:

\[ F = m \cdot a \]

This shows that the net external force acting on an object is equal to the mass of the object multiplied by its acceleration.

### Step 5: Analyze the Options
Now, let's analyze the options provided in the question:
1. Momentum and acceleration
2. Change in momentum and velocity
3. Rate of change of momentum and external force
4. Rate of change of force and momentum

From our understanding of Newton's second law, the correct connection is:

**Rate of change of momentum and external force.**

### Conclusion
Thus, the correct answer to the question is option 3: "Rate of change of momentum and external force."

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