Which one of the following statements is not true

Options

A. The same force for the same time causes the same change in momentent for different bodies.
B. The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.
C. A greater opposing force is needed to stop a heavy body than a light body in the same time, if they are moving with the same speed.
D. The greater the change in the momentum in a given time, is the forece that needs to be applied.

Explanation

To solve the question of which statement is not true, we will analyze each statement one by one based on the principles of momentum and Newton's laws of motion.

### Step-by-Step Solution:

1. **Analyze the First Statement**:
- **Statement**: "The same force for the same time causes the same change in momentum for different bodies."
- **Analysis**: According to the impulse-momentum theorem, the impulse (force multiplied by time) equals the change in momentum. However, if different bodies have different masses, the same force applied for the same time will result in different changes in momentum. Therefore, this statement is **not true**.

2. **Analyze the Second Statement**:
- **Statement**: "The rate of change of momentum of a body is strictly proportional to the applied force and takes place in the direction in which the force acts."
- **Analysis**: This statement is a restatement of Newton's second law of motion, which is true. The rate of change of momentum is indeed proportional to the force applied.

3. **Analyze the Third Statement**:
- **Statement**: "A greater opposing force is needed to stop a heavy body than a light body in the same time if they are moving with the same speed."
- **Analysis**: This statement is also true. A heavier body has more momentum (mass times velocity) than a lighter body moving at the same speed, thus requiring a greater force to stop it in the same amount of time.

4. **Analyze the Fourth Statement**:
- **Statement**: "The greater the change in momentum in a given time, the greater the force that needs to be applied."
- **Analysis**: This statement is true as well. According to the formula \( F = \frac{dP}{dt} \), a greater change in momentum over a given time indeed requires a greater force.

### Conclusion:
After analyzing all four statements, the first statement is the one that is **not true**.

### Final Answer:
The statement that is not true is: "The same force for the same time causes the same change in momentum for different bodies."

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