Which one of the following statement is not ture about Newton's second law of motion `vec(F)=vec(ma)` ?

Options

A. 1. The second law of motion is consistent with the first law
B. 2. The second law of motion is a vector law.
C. 3. The second law of motion is applicable to a single point particle.
D. 4. The second law of motion is not applicable to a single point particle.

Explanation

To determine which statement is not true about Newton's second law of motion, we will analyze each option provided in the question. The second law is mathematically expressed as \(\vec{F} = m\vec{a}\), where \(\vec{F}\) is the net force acting on an object, \(m\) is the mass of the object, and \(\vec{a}\) is the acceleration produced.

### Step-by-Step Solution:

1. **Understanding Newton's Second Law**:
- Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that if a net force is applied to an object, it will accelerate in the direction of the force.

2. **Analyzing the Statements**:
- We need to evaluate the truth of each statement regarding Newton's second law.

- **Option 1**: "The second law is consistent with the first law."
- This statement is true. The first law states that an object at rest stays at rest, and an object in motion stays in motion unless acted upon by a net external force. This is consistent with the second law, as it implies that if no force is applied (\(F = 0\)), the acceleration (\(a\)) will also be zero, maintaining the state of rest or uniform motion.

- **Option 2**: "The second law is a vector law."
- This statement is also true. Force and acceleration are vector quantities, meaning they have both magnitude and direction. Therefore, the second law, which involves these quantities, is indeed a vector law.

- **Option 3**: "The second law is applicable to a single point."
- This statement is true. Newton's second law can be applied to a single point particle, where the net force acting on that particle results in acceleration.

- **Option 4**: "The second law of motion is not applicable to a single point particle."
- This statement is false. The second law is specifically applicable to single point particles, as it describes how they respond to forces.

3. **Conclusion**:
- The statement that is not true about Newton's second law of motion is **Option 4**: "The second law of motion is not applicable to a single point particle."

### Final Answer:
**Option 4** is the statement that is not true about Newton's second law of motion.